ORIGINAL_ARTICLE
Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multi-frames (resp. multi-Riesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.
https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf
2019-07-01
1
18
10.22130/scma.2018.77908.356
Multi-frame vector
Wandering vector
Local commutant
Unitary system
Mohammad
Mahmoudieh
mahmoudieh@du.ac.ir
1
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
AUTHOR
Hessam
Hosseinnezhad
hosseinnezhad_h@yahoo.com
2
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
AUTHOR
Gholamreza
Abbaspour Tabadkan
abbaspour@du.ac.ir
3
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
LEAD_AUTHOR
[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert space, Ann. Physics., 222 (1993), pp. 1-37.
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[2] B.K. Alpert, A class of bases in $L^2$ for the sparse representation of integral operators, SIAM J. Math. Anal., 24 (1993), pp. 246-262.
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[3] L. Arambasic, On frames for countably generated Hilbert $C^*$-modules, Proc. Amer. Math. Soc., 135 (2007), pp. 469-478.
3
[4] D. Bakic and B. Guljas, Hilbert $C^*$-modules over $C^*$-algebras of compact operators, Acta Sci. Math. (Szeged), 68 (2002), pp. 249-269.
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[5] P. Balazs, M. D"orfler, N. Holighaus, F. Jaillet, and G. Velasco, Theory, implementation and applications of nonstationary Gabor frames, J. Comput. Appl. Math., 236 (2011), pp. 1481-1496.
5
[6] P. Balazs, B. Laback, G. Eckel, and W.A. Deutsch, Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking, IEEE Trans. Audio. Speech. Language Process., 18 (2010), pp. 34-49.
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[9] P. Casazza and G. Kutyniok, Finite Frames: Theory And Applications, Springer Science & Business Media, Birkhauser, 2012.
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[11] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2016.
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[12] O. Christensen and D. Stoeva, $p$-frames in separable Banach spaces, Adv. Comput. Math., 18 (2003), pp. 117-126.
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[13] N. Cotfas and J.P. Gazeau, Finite tight frames and some applications, J. Phys. A., 43 (2010), p. 193001.
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[14] S. Dahlke, M. Fornasier, and T. Raasch, Adaptive Frame Methods for Elliptic Operator Equations, Adv. Comput. Math., 27 (2007), pp. 27-63.
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[15] X. Dai and D.R. Larson, Wandering vectors for unitary systems and orthogonal wavelets, Amer. Math. Soc., 640, 1998.
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[18] M. Dorfler and H. Feichtinger, Quilted Gabor families I: Reduced multi-Gabor frames, Appl. Comput. Harmon. Anal., 356 (2004), pp. 2001-2023.
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[19] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
19
[20] M. Frank and D. Larson, Frames in Hilbert $C^*$-modules and $C^*$-algebras, J. Operator Theory., 48 (2002), pp. 273-314.
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[25] L. Herve, Multi-resolution analysis of multiplicity d: applications to dyadic interpolation, Appl. Comput. Harmon. Anal., 1 (1994), pp. 299-315.
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[26] W. Jing, Frames in Hilbert $C^*$-modules, Ph.D. Thesis, University of Central Florida, 2006.
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[30] P. Majdak, P. Balazs, W. Kreuzer, and M. Dorfler, A time-frequency method for increasing the signal-to-noise ratio insystem identification with exponential sweeps, In: Proceedings of the 36th International Conference on Acoustics, Speech and Signal Processing, ICASSP 2011, Prag, 2011, 3812-3815.
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[31] V.M. Manuilov and E.V. Troitsky, Hilbert $C^*$modules, Amer. Math. Soc., 2005.
31
[32] R. Stevenson, Adaptive solution of operator equations using wavelet frames, SIAM J. Numer. Anal., 41 (2003), pp. 1074-1100.
32
ORIGINAL_ARTICLE
A Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type
In this paper, we generalize the Meir-Keeler condensing operators via a concept of the class of operators $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems. As an application of this extension, we analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally, we present an example to show the effectiveness of our results. We use the technique of measure of noncompactness to obtain our results.
https://scma.maragheh.ac.ir/article_34954_fb1f8292e46d2d8e27e2ad9e34eb5f31.pdf
2019-07-01
19
35
10.22130/scma.2018.74869.322
Measure of noncompactness
Fixed point theorem
Integral equations
Shahram
Banaei
sh_banaei@yahoo.com
1
Department of Mathematics, Bonab Branch, Islamic Azad University, Bonab, Iran.
AUTHOR
Mohammad Bagher
Ghaemi
mghaemi@iust.ac.ir
2
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
LEAD_AUTHOR
[1] R. Agarwal, M. Meehan, and D. O'Regan, Fixed point theory and applications, Cambridge University Press, 2004.
1
[2] A. Aghajani, J. Banas, and Y. Jalilian, Existence of solution for a class nonlinear Voltrra sigular integral, Appl. Math. Comput., 62 (2011), pp. 1215-1227.
2
[3] A. Aghajani, M. Mursaleen, and A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measures of noncompactness, Acta Mathematica Scientia., 35 (2015), pp. 552-566.
3
[4] I. Altun and D. Turkoglu, A fixed point theorem for mappings satisfying a general contractive condition of operator type, Journal of Computational Analysis and Applications., 9 (2007), pp. 9-14.
4
[5] R. Arab, R. Allahyari, and A. Shole Haghighi, Construction of a Measure of Noncompactness on BC($Omega$) and its Application to Volterra Integral Equations, Mediterr. J. Math., 13 (2016), pp. 1197-1210.
5
[6] Sh. Banaei, M.B. Ghaemi, and R. Saadati, An extension of Darbo's theorem and its application to system of neutral diferential equations with deviating argument, Miskolc Mathematical Notes, 18 (2017), pp. 83-94.
6
[7] J. Banas, M. Jleli, M. Mursaleen, and B. Samet, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, Springer, Singapore, 2017.
7
[8] J. Banas and K. Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, New York, 1980.
8
[9] J. Banas, D. O'regan, and K. Sadarangani, On solutions of a quadratic hammerstein integral equation on an unbounded interval, Dynam. Systems Appl., 18 (2009), pp. 251-264.
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[10] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova., 24 (1955), pp. 84-92.
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[11] M.A. Darwish, Monotonic solutions of a convolution functional integral equation, Appl. Math. Comput., 219 (2013), pp. 10777-10782.
11
[12] V. Karakaya, N. El Houda Bouzara, and Y. Atalan, Existence of tripled fixed points for a class of condensing operators in banach spaces, The Scientific World Journal, (2014), pp. 1-9.
12
[13] K. Kuratowski, Sur les espaces, Fund. Math., 15 (1930), pp. 301-309.
13
[14] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math Anal Appl., 28 (1969), pp. 326-329.
14
[15] M. Mursaleen and S.A. Mohiuddine, Applications of measures of noncompactness to the infinite system of differential equations in $l_p$ spaces, Nonlinear Analysis., 75 (2012), pp. 2111-2115.
15
[16] L. Olszowy, Solvability of infinite systems of singular integral equations in Frechet space of continuous functions, Computers and Mathematics with Applications, 59 (2010), pp. 2794-2801.
16
[17] A. Samadi and Mohammad B. Ghaemi, An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations, Filomat., 28 (2014), pp. 879-886.
17
[18] B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Analysis, 72 (2010), pp. 4508-4517.
18
ORIGINAL_ARTICLE
Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces
In this paper, we introduce $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frames is a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel multiplier is a p-Schatten class operator.
https://scma.maragheh.ac.ir/article_34963_35384b34dcf883a65808ec86a7f3b34c.pdf
2019-07-01
37
48
10.22130/scma.2019.68582.264
Controlled continuous $g$-frames
$(mathcal{C}
mathcal{C}')$-controlled continuous $g$-Bessel families
Multiplier of continuous $g$-frames
Yahya
Alizadeh
ya.alizadeh@gmail.com
1
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.
AUTHOR
Mohammad Reza
Abdollahpour
mrabdollahpour@yahoo.com
2
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.
LEAD_AUTHOR
[1] M.R. Abdollahpour and Y. Alizadeh, Multipliers of Continuous $G$-Frames in Hilbert spaces, Bull. Iranian. Math. Soc., 43 (2017), pp. 291-305.
1
[2] M.R. Abdollahpour and M.H. Faroughi, Continous g-Frames in Hilbert spaces, Southeast asian Bulletin of Mathematics, 32 (2008), pp. 1-19.
2
[3] P. Balazs, Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (2007), pp. 571-585.
3
[4] P. Balazs, J.P. Antoine, and A. Grybos, Weighted and controlled frames, Int. J. Wavelets Multiresolut Inf. Prosses., 8 (2010), pp. 109-132.
4
[5] P. Balazs, D. Bayer, and A. Rahimi, Multipliers for continuous frames in Hilbert spaces, J. Phys. A: Math. Theory., 45 (2012), pp. 1-20.
5
[6] I. Bogdanova, P. Vandergheynst, J.P. Antoine, L. Jacques, and M. Morvidone, Stereographic wavelet frames on sphere, Applied Comput. Harmon. Anal., 19 (2005), pp. 223-252.
6
[7] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser Boston, 2003.
7
[8] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier seris, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
8
[9] L.O. Jacques, Reperes et couronne solaire, These de Doctorat, Univ. Cath. Louvain, Louvain-la-Neuve. 2004.
9
[10] G.J. Murphy, $C^*$-algebras and operator theory, Academic Press Inc., 1990.
10
[11] A. Rahimi and A. Fereydooni, Controlled $G$-Frames and Their $G$-Multipliers in Hilbert spaces, An. St. Univ. Ovidius Constanta, versita., 21 (2013), pp. 223-236.
11
[12] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
12
ORIGINAL_ARTICLE
Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.
https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf
2019-07-01
49
63
10.22130/scma.2018.74791.321
MRA
Heat equation
wavelet method
Finite difference
Zahra
Kalateh Bojdi
z.kalatehbojdi@student.kgut.ac.ir
1
Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.
AUTHOR
Ataollah
Askari Hemmat
askari@uk.ac.ir
2
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
LEAD_AUTHOR
Ali
Tavakoli
a.tavakoli@umz.ac.ir
3
Mathematics department, University of Mazandaran, Babolsar, Iran.
AUTHOR
[1] G. Beylkin, Wavelets and Fast Numerical Algorithms, Lecture Notes for Short Course, Amer. Math. Soc., Rhode Island, 1993.
1
[2] G. Beylkin and N. Saito, Wavelets, their autocorrelation functions, and multiresolution representation of signals, Expanded abstract in Proceedings ICASSP-92, 4 (1992), pp. 381-384.
2
[3] C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral Methods: Fundamentals in Single Domains, Berlin, Springer, 2006.
3
[4] C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral Methods in Fluid Dynamics, Berlin, Springer Series in Computational Physics, 1988.
4
[5] G. Chen, Semi-analytical solutions for 2-D modeling of long pulsed laser heating metals with temperature dependent surface absorption, Optik, International Journal for Light and Electron Optics, 2017.
5
[6] RJ. Chiffell, On the wave behavior and rate effect of thermal and thermo-mechanical waves, M.Sc. Thesis, University of New Mexico, Albuquerque, 1994.
6
[7] W. Dai, F. Han, and Z. Sun, Accurate Numerical Method for Solving Dual-Phase-Lagging Equation with Temperature Jump Boundary Condition in Nano Heat Conduction, Int. J. Heat Mass Transf., 64 (2013), pp. 966-975.
7
[8] W. Dai and R. Nassar, A compact finite difference scheme for solving a one-dimensional heat transport equation at the microscale, J. Comput. Appl. Math., 132 (2001), pp. 431-441.
8
[9] W. Dai and R. Nassar, A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film, Numer. Methods Partial Differ. Equ., 16 (2000), pp. 441-458.
9
[10] W. Dai and R. Nassar, A finite difference method for solving the heat transport equation at the microscale, Numer. Methods Partial Differ. Equ., 15 (1999), pp. 697-708.
10
[11] W. Dai and R. Nassar, A finite difference scheme for solving a three-dimensional heat transport equation in a thin film with microscale thickness, Internat. J. Numer. Methods Engrg., 50 (2001), pp. 1665-1680.
11
[12] I. Daubechies, Ten Lectures on Wavelets, Soc. for Indtr. Appl. Math., Philadelphia, Number 61, 1992.
12
[13] J. Fan and L. Wang, Analytical theory of bioheat transport, J. Appl. Phys., 109 (2011).
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[14] Z-Y. Guo and Y-S. Xu, Non-Fourier Heat Conduction in IC Chip, ASME J. Electron Packag., 117 (1995), pp. 174-177.
14
[15] Z. Kalateh Bojdi and A. Askari Hemmat, Wavelet collocation methods for solving the Pennes bioheat transfer equation, Optik, Int. J. Light Electron Optics, 132 (2017), pp. 80-88.
15
[16] Z. Kargar and H. Saeedi, B-spline wavelet operational method for numerical solution of time-space fractional partial differential equations, Int. J. Wavelets Multiresolut. Inf. Process., 15 (2017), 1750034.
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[17] A. Latto, L. Resnikoff, and E. Tenenbaum, The evaluation of connection coefficients of compactly supported wavelets, Proceedings of the French-USA Workshop on Wavelets and Turbulence, 1992, pp. 76-89.
17
[18] A. Malek, Z. Kalateh Bojdi, and P. Nuri Niled Gobarg, Solving Fully three-Dimensional Micros cal Dual Phase Lag Problem Using Mixed-Collocation, Finite Difference Discretization, Trans. ASME J. Heat Transf., 134 (2012).
18
[19] A. Malek and SH. Momeni-Masuleh, A Mixed Collocation-Finite Difference Method for 3D Microscopic Heat Transport Problems, J. Comput. Appl. Math., 217 (2008), pp. 137-147.
19
[20] A. Malek and S.H. Momeni-Masuleh, A Mixed Collocation-Finite Difference Method for 3D Microscopic Heat Transport Problems, J. Comput. Appl. Math., 217 (2008), pp. 137-147.
20
[21] S. Mallat, Multiresolution approximation and wavelets, Preprint GRASP Lab., Dept. of Computer and Information Science, Univ. of Pennsylvania, 1987.
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[22] T.Q. Qui and C.L. Tien, Short-pulse laser heating on metals, Int. J. Heat Mass Transf., 35 (1992), pp. 719-726.
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[23] T.Q. Qui and C.L. Tien, Heat transfer mechanisms during short-pulse laser heating on metals, ASME J. Heat Transf., 115 (1993), pp. 835-841.
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[24] G.D. Smith, Numerical Solution of Partial Differential Equations Finite Difference Methods, Third ed., Oxford, Oxford University Press, 1985.
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[25] D.Y. Tzou, Macro to Micro Heat Transfer, Washington, Taylor and Francis, 1996.
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[26] R. Viskanta and T.L. Bergman, Heat Transfer in Materials Processing, Third Edition, New York, McGraw-Hill Book Company, 1998.
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[27] D. Xue, Three-dimensional simulation of the temperature field in high-power double-clad fiber laser, Optik, Int. J. Light Electron Optics, (2011).
27
[28] J. Zhang and J.J. Zhao, Iterative solution and finite difference approximations to 3D microscale heat transport equation, Math. Comput. Simulation, 57 (2001), pp. 387-404.
28
ORIGINAL_ARTICLE
Theory of Hybrid Fractional Differential Equations with Complex Order
We develop the theory of hybrid fractional differential equations with the complex order $\theta\in \mathbb{C}$, $\theta=m+i\alpha$, $0<m\leq 1$, $\alpha\in \mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $\mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schr\"odinger equation with complex order is given.
https://scma.maragheh.ac.ir/article_34967_a19fd276ba6778bbb6bed7f43599acca.pdf
2019-07-01
65
76
10.22130/scma.2018.72907.295
Hybrid fractional differential equations
Initial value problem
Complex order
Dhage's fixed point theorems
Existence of mild solution
Devaraj
Vivek
peppyvivek@gmail.com
1
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
AUTHOR
Omid
Baghani
omid.baghani@gmail.com
2
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
LEAD_AUTHOR
Kuppusamy
Kanagarajan
kanagarajank@gmail.com
3
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
AUTHOR
[1] B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal., (2014), Article ID 705809, 7 pages.
1
[2] B. Ahmad and S.K. Ntouyas, Initial value problems for hybrid Hadamard fractional differential equations, Electron. J. Diff. Eq., 161 (2014), pp. 1-8.
2
[3] R. Andriambololona, R. Tokiniaina, and H. Rakotoson, Definitions of complex order integrals and complex order derivatives using operator approach, Int. J. Latest Res. Sci. Tech., 1 (2012), pp. 317-323.
3
[4] T.M. Atanackovic, S. Konjik, S. Pilipovic, and D. Zorica, Complex order fractional derivatives in viscoelasticity, Mech. Time-Depend. Mater., 1 (2016), pp. 1-21.
4
[5] O. Baghani, On fractional Langevin equation involving two fractional orders, Commun. Nonlinear
5
Sci. Numer. Simulat., 42 (2017), pp. 675-681.
6
[6] B.C. Dhage, On a fixed point theorem in Banach algebras with applications, Appl. Math. Lett., 18 (2005), pp. 273-280.
7
[7] B.C. Dhage, On some variants of Schauder's fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci., 25 (1988), pp. 603-611.
8
[8] B.C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst., 4 (2010), pp. 414-424.
9
[9] P. Gorka, H. Prado, and J. Trujillo, The time fractional Schr"odinger equation on Hilbert space, Integr. Equ. Oper. Theory, 88 (2017), pp. 1-14.
10
[10] M.A.E. Herzallah and D. Baleanu, On fractional order hybrid differential equations, Abst. Appl. Anal., 2014, Article ID 389386, 7 pages.
11
[11] R. Hilfer, Application of Fractional Calculus in Physics, World Scientific, Singapore, 1999.
12
[12] A.A. Kilbas, H.M. Srivasta, and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier B. V., Netherlands, 2016.
13
[13] N. Kosmatov, Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear Anal., 70 (2009), pp. 2521-2529.
14
[14] E.R. Love, Fractional derivatives of imaginary order, J. London Math. Soc., 2 (1971), pp. 241-259.
15
[15] A. Neamaty, M. Yadollahzadeh, and R. Darzi, On fractional differential equation with complex order, Progr. Fract. Differ. Appl., 1 (2015), pp. 223-227.
16
[16] C.M.A. Pinto and J.A.T. Machado, Complex order Van der Pol oscillator, Nonlinear Dyn., 65 (2011), pp. 247-254.
17
[17] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
18
[18] B. Ross and F. Northover, A use for a derivative of complex order in the fractional calculus, Int. J. Pure Appl. Math., 9 (1978), pp. 400-406.
19
[19] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Philadelphia, 1993.
20
[20] D. Vivek, K. Kanagarajan, and S. Harikrishnan, Dynamics and stability results for integro-differential equations with complex order, Discontinuity, Nonlinearity and Complexity, In Press, 2018.
21
[21] D. Vivek, K. Kanagarajan, and S. Harikrishnan, Dynamics and stability results for pantograph equations with complex order, Journal of Applied Nonlinear Dynamics, 7 (2018), pp. 179-187.
22
[22] Y. Zhao, S. Sun, Z. Han, and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), pp. 1312-1324.
23
ORIGINAL_ARTICLE
$\sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras
In this paper, pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $\ell^1(S,\omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $\ell^1(G,\omega)$ are the same. Examples are given to show that the class of $\sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.
https://scma.maragheh.ac.ir/article_34969_62c81b96df381db750dd155bb9dd2dbb.pdf
2019-07-01
77
89
10.22130/scma.2018.73939.308
$sigma$-Connes amenability
Pseudo-amenability
Pseudo-Connes amenability
Beurling algebras
Zahra
Hasanzadeh
zh_hasanzadeh@yahoo.com
1
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
AUTHOR
Amin
Mahmoodi
a_mahmoodi@iauctb.ac.ir
2
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
LEAD_AUTHOR
[1] H.G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.
1
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[6] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability, II, J. Funct. Anal., 254 (2008), pp. 1776-1810.
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18
ORIGINAL_ARTICLE
Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces
Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions. The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach contraction principle is that it also gives the convergence of an iterative scheme to a unique fixed point. In this paper, we consider $(X, M, *)$ to be fuzzy metric spaces in Park's sense and we show our results for fixed points of contractive and nonexpansive multifunctions on Hausdorff fuzzy metric space.
https://scma.maragheh.ac.ir/article_35070_810d28ad9c75d6e7f96342191446473e.pdf
2019-07-01
91
106
10.22130/scma.2018.72350.288
Inexact iterative
Fixed point
Contraction multifunction
Hausdorff fuzzy metric
Mohammad Esmael
Samei
me_samei@yahoo.com
1
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, 6517838695, Hamedan, Iran.
LEAD_AUTHOR
[1] R.P. Agarwal, M.A. El-Gebeily, and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Analysis, 87 (2008), pp. 109-116.
1
[2] I. Altun and G. Durmaz, Some fixed point results in cone metric spaces, Rend Circ. Math. Palermo, 58 (2009), pp. 319-325.
2
[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), pp. 133-181.
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[4] V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Analysis, 74 (2011), pp. 7347-7355.
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[6] C. Di Bari and C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend Circ. Math. Palermo, 52 (2003), pp. 315-321.
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[8] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), pp. 385-389.
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[9] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), pp. 245-252.
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[11] H. Karayilan and M. Telci, Common fixed point theorem for contractive type mappings in fuzzy metric spaces, Rend. Circ. Mat. Palermo., 60 (2011), pp. 145-152.
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[15] D. Mihet, A banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), pp. 431-439.
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[16] J.H. Park, Intiutionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), pp. 1039-1046.
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[17] J.S. Park, Y.C. Kwun, and J.H. Park, A fixed point theorem in the intiutionistic fuzzy metric spaces, Far East J. Math. Sci. 16 (2005), pp. 137-149.
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[18] M. Rafi and M.S.M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces, Iranian J. of Fuzzy Systems, 3 (2006), pp. 23-29.
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[19] D. Reem, S. Reich, and A. Zaslavski, Two results in metric fixed point theory, J. Fixed Point Theory Appl. 1 (2007), pp. 149-157.
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[20] Sh. Rezapour and P. Amiri, Some fixed point results for multivalued operators in generalized metric spaces, Computers and Mathematics with Applications 61 (2011), pp. 2661-2666.
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[21] Sh. Rezapour and R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Analysis Appl. 345 (2008), pp. 719-724.
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[22] J. Rodrigues-Lopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), pp. 273-283.
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[23] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), pp. 1861-1869.
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[24] P. Veeramani, Best approximation in fuzzy metric spaces, J. Fuzzy Math., 9 (2001), pp. 75-80.
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[25] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), pp. 338-353.
25
ORIGINAL_ARTICLE
Bounded Approximate Character Amenability of Banach Algebras
The bounded approximate version of $\varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded approximate character amenability of some Banach algebras related to locally compact groups are investigated.
https://scma.maragheh.ac.ir/article_35435_9d883ba7e3298bfb19d2cc5f830fe1a2.pdf
2019-07-01
107
118
10.22130/scma.2018.79315.372
Banach algebras
Bounded approximate character amenability
Bounded approximate character contractibility
Locally compact groups
Hasan
Pourmahmood Aghababa
hpaghababa@tabrizu.ac.ir
1
Department of Mathematics, University of Tabriz, Tabriz, Iran.
AUTHOR
Fourogh
Khedri
f.khedri@azaruniv.edu
2
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
AUTHOR
Mohammad Hossein
Sattari
sattari@azaruniv.ac.ir
3
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
LEAD_AUTHOR
[1] H.P. Aghababa, L.Y. Shi, and Y.J. Wu, Generalized notions of character amenability, Acta Math. Sin. (Engl. Ser.), 29 (2013), pp. 1329-1350.
1
[2] Y. Choi, F. Ghahramani, and Y. Zhang, Approximate and pseudo-amenability of various classes of Banach algebras, J. Funct. Anal., 256 (2009), pp. 3158-3191.
2
[3] B. Dorofaeff, The Fourier algebra of SL(2, R)?R^n, n≥2, has no multiplier bounded approximate unit, Math. Ann., 297 (1993), pp. 707-724.
3
[4] F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208 (2004), pp. 229-260.
4
[5] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability II, J. Funct. Anal., 254 (2008), pp. 1776-1810.
5
[6] F. Ghahramani and C.J. Read, Approximate identities in approximate amenability, J. Funct. Anal., 262 (2012), pp. 3929-3945.
6
[7] U. Haagerup, An example of a nonnuclear $C^*$-algebra, which has the metric approximation property, Invent. math., 50 (1978/79), pp. 279-293.
7
[8] C. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble), 23 (1973), pp. 91-123.
8
[9] Z. Hu, M.S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (2009), pp. 53-78.
9
[10] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972), pp. 1-96.
10
[11] E. Kaniuth, A.T. Lau, and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl., 344 (2008), pp. 942-955.
11
[12] M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 697-706.
12
ORIGINAL_ARTICLE
Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Let $ \mathcal{H}(\mathbb{D}) $ denote the space of analytic functions on the open unit disc $\mathbb{D}$. For a weight $\mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ \mathcal{W}_\mu ^{(n)} $ is the space of all $f\in \mathcal{H}(\mathbb{D}) $ such that $\sup_{z\in \mathbb{D}}\mu(z)\left|f^{(n)}(z)\right|<\infty.$ Endowed with the norm \begin{align*}\left\|f \right\|_{\mathcal{W}_\mu ^{(n)}}=\sum_{j=0}^{n-1}\left|f^{(j)}(0)\right|+\sup_{z\in \mathbb{D}}\mu(z)\left|f^{(n)}(z)\right|,\end{align*}the $n$'th weighted type space is a Banach space. In this paper, we characterize the boundedness of generalized weighted composition operators $\mathcal{D}_{\varphi ,u}^m$ from logarithmic Bloch type spaces $\mathcal{B}_{{{\log }^\beta }}^\alpha $ to $n$'th weighted type spaces $ \mathcal{W}_\mu ^{(n)} $, where $u$ and $\varphi$ are analytic functions on $\mathbb{D}$ and $\varphi(\mathbb{D})\subseteq\mathbb{D}$. We also provide an estimation for the essential norm of these operators.
https://scma.maragheh.ac.ir/article_35724_a056298520b5f4f883e2417d01c90dcb.pdf
2019-07-01
119
133
10.22130/scma.2018.78754.365
Essential norms
Generalized weighted composition operators
Logarithmic Bloch type spaces
$N$th weighted type spaces
Kobra
Esmaeili
esmaeili@ardakan.ac.ir
1
Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.
LEAD_AUTHOR
[1] K. Attele, Toeplitz and Hankel operators on Bergman one space, Hokkaido Math. J., 21 (1992), pp. 279-293.
1
[2] K.D. Bierstedt, J. Bonet, and J. Taskinen, Associated weights and spaces of holomorphic functions, Stud. Math., 127 (1998), pp. 137-168.
2
[3] J. Bonet, P. Domanski, and M. Lindstrom, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull., 42 (1999), pp. 139-148.
3
[4] L. Brown and A.L. Shields, Multipliers and cyclic vectors in the Bloch space, Michigan Math. J., 38 (1991), pp. 141-146.
4
[5] K. Esmaeili and M. Lindstrom, Weighted composition operators between Zygmund type spaces and their essential norms, Integr. Equ. Oper. Theory, 75 (2013), pp. 473-490.
5
[6] O. Hyvarinen, M. Kemppainen, M. Lindstrom, A. Rautio, and E. Saukko, The essential norms of weighted composition operators on weighted Banach spaces of analytic function, Integr. Equ. Oper. Theory, 72 (2012), pp. 151-157.
6
[7] B. MacCluer and R. Zhao, Essential norms of weighted composition operators between Bloch-type spaces, Rocky Mount. J. Math., 33 (2003), pp. 1437-1458.
7
[8] A. Montes-Rodriguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. (3), 61 (2000), pp. 872-884.
8
[9] S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mount. J. Math., 33 (2003), pp. 191-215.
9
[10] H. Qu, Y. Liu, and S. Cheng, Weighted differentiation composition operator from logarithmic Bloch spaces to Zygmund-type spaces, Abstr. Appl. Anal., 2014, Art. ID 832713, 14 pp.
10
[11] J.C. Ramos-Fernandez, Logarithmic Bloch spaces and their weighted composition operators, Rend. Circ. Mat. Palermo (2), 65 (2016), pp. 159-174.
11
[12] S. Stevic, On new Bloch-type spaces, Appl. Math. Comput., 215 (2009), pp. 841-849.
12
[13] S. Stevic, Weighted differentiation composition operators from H∞ and Bloch spaces to nth weighted-type spaces on the unit disk, Appl. Math. Comput., 216 (2010), pp. 3634-3641.
13
[14] S. Stevic and A.K. Sharma, Iterated differentiation followed by composition from Bloch-type spaces to weighted BMOA spaces, Appl. Math. Comput., 218 (2011), pp. 3574-3580.
14
[15] M. Tjani, Compact composition operators on some Mobius invariant Banach spaces [Ph.D. thesis], Michigan State University, 1996.
15
[16] R. Yoneda, The composition operators on weighted Bloch space, Arch. Math. (Basel), 78 (2002), pp. 310-317.
16
[17] K. Zhu, Bloch type spaces of analytic functions, Rocky Mount. J. Math., 23 (1993), pp. 1143-1177.
17
[18] X. Zhu, Generalized weighted composition operators from Bers- type spaces into Bloch-type spaces, Math. Inequal. Appl., 17 (2014), pp. 187-195.
18
[19] X. Zhu, Products of differentiation, composition and multiplication from Bergman type spaces to bers type space, Integ. Tran. Spec. Funct., 18 (2007), pp. 223-231.
19
ORIGINAL_ARTICLE
Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^\ast-$modules
In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^\ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^\ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.
https://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf
2019-07-01
135
146
10.22130/scma.2018.81624.396
Frame
$g$-frame
Fusion frame
Biorthogonal sequence
Approximate duality
Morteza
Mirzaee Azandaryani
morteza_ma62@yahoo.com
1
Department of Mathematics, University of Qom, Qom, Iran.
LEAD_AUTHOR
[1] L. Arambasic, On frames for countably generated Hilbert $C^ast-$modules, Proc. Amer. Math. Soc., 135 (2007), pp. 469-478.
1
[2] P. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math. Amer. Math. Soc., 345 (2004), pp. 87-113.
2
[3] O. Christensen and R.S. Laugesen, Approximate dual frames in Hilbert spaces and applications to Gabor frames, Sampl Theory Signal Image Process., 9 (2011), pp. 77-90.
3
[4] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283.
4
[5] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
5
[6] M. Frank and D. Larson, Frames in Hilbert $C^ast-$modules and $C^ast-$algebras, J. Operator Theory., 48 (2002), pp. 273-314.
6
[7] D. Han, W. Jing, D. Larson, and R. Mohapatra, Riesz bases and their dual modular frames in Hilbert $C^ast$--modules, J. Math. Anal. Appl., 343 (2008), pp. 246-256.
7
[8] S.B. Heineken, P.M. Morillas, A.M. Benavente, and M.I. Zakowicz, Dual fusion frames, Arch. Math., 103 (2014), pp. 355-365.
8
[9] A. Khosravi and B. Khosravi, Fusion frames and $g$-frames in Hilbert $C^ast-$modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), pp. 433-446.
9
[10] A. Khosravi and B. Khosravi, G-frames and modular Riesz bases, Int. J. Wavelets Multiresolut. Inf. Process., 10 (2012), pp. 1-12.
10
[11] A. Khosravi and M. Mirzaee Azandaryani, Approximate duality of $g$-frames in Hilbert spaces, Acta. Math. Sci., 34 (2014), pp. 639-652.
11
[12] E.C. Lance, Hilbert $C^ast-$modules: A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge., 1995.
12
[13] M. Mirzaee Azandaryani, Approximate duals and nearly Parseval frames, Turk. J. Math., 39 (2015), pp. 515-526.
13
[14] M. Mirzaee Azandaryani, Bessel multipliers and approximate duals in Hilbert $C^ast-modules$, J. Korean Math. Soc., 54 (2017), pp. 1063-1079.
14
[15] M. Mirzaee Azandaryani, On the approximate duality of $g$-frames and fusion frames, U. P. B. Sci. Bull. Ser A., 79 (2017), pp. 83-93.
15
[16] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
16
[17] X. Xiao and X. Zeng, Some properties of $g$-frames in Hilbert $C^ast$--modules, J. Math. Anal. Appl., 363 (2010), pp. 399-408.
17
ORIGINAL_ARTICLE
Primitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(\mathcal G)$ associated to the ultragraph $\mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*\left(\mathcal G/(H,S)\right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the Hong and Szyma$ \acute{ \mathrm { n } } $ski's description of the primitive ideal space of a graph $ C ^ * $-algebra by a simpler method.
https://scma.maragheh.ac.ir/article_35729_73ba5420990970a0ddcac2ce5d817221.pdf
2019-07-01
147
158
10.22130/scma.2018.82725.404
Ultragraph
Ultragraph $C^*$-algebra
Primitive ideal
Mostafa
Imanfar
m.imanfar@aut.ac.ir
1
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
AUTHOR
Abdolrasoul
Pourabbas
arpabbas@aut.ac.ir
2
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
LEAD_AUTHOR
Hossein
Larki
h.larki@scu.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran.
AUTHOR
[1] G. Abrams, P. Ara, and M. Siles Molina, Leavitt Path Algebras, Lecture Notes in Mathematics Vol. 2191, Springer, London, 2017.
1
[2] T. Bates, D. Pask, I. Raeburn, and W. Szymanski, The $C^*$-algebras of row-finite graphs, New York J. Math., 6 (2000), pp. 307-324.
2
[3] T.M. Carlsen, S. Kang, J. Shotwell, and A. Sims, The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources, J. Funct. Anal., 266 (2014), pp. 2570-2589.
3
[4] T.M. Carlsen and A. Sims, On Hong and Szymanski's description of the primitive-ideal space of a graph algebra, Operator algebras and applicationsthe Abel Symposium (2015), Abel Symp., 12, Springer, [Cham], (2017), pp. 115-132.
4
[5] J. Cuntz and W. Krieger, A class of $C^*$-algebras and topological Markov chains, Invent. Math., 56 (1980), pp. 251-268.
5
[6] R. Exel and M. Laca, Cuntz-Krieger algebras for infinite matrices, J. Reine Angew. Math., 512 (1999), pp. 119-172.
6
[7] N. Fowler, M. Laca, and I. Raeburn, The $C^*$-algebras of infinite graphs, Proc. Amer. Math. Soc., 128 (2000), pp. 2319-2327.
7
[8] J. Hong and W. Szymanski, The primitive ideal space of the $C^*$-algebras of infinite graphs, J. Math. Soc. Japan, 56 (2004), pp. 45-64.
8
[9] T. Katsura, P.S. Muhly, A. Sims, and M. Tomforde, Utragraph $C^*$-algebras via topological quivers, Studia Math., 187 (2008), pp. 137-155.
9
[10] A. Kumjian, D. Pask, and I. Raeburn, Cuntz-Krieger algebras of directed graphs, Pacific J. Math., 184 (1998), pp. 161-174.
10
[11] H. Larki, Primitive ideals and pure infiniteness of ultragraph $C^*$-algebras, J. Korean Math. Soc., 56 (2019), pp. 1-23.
11
[12] H. Larki, Primitive ideal space of higher-rank graph $C^*$-algebras and decomposability, J. Math. Anal. Appl., 469 (2019), pp. 76-94.
12
[13] M. Tomforde, A unified approach to Exel-Laca algebras and $C^*$-algebras associated to graphs, J. Operator Theory, 50 (2003), pp. 345-368.
13
ORIGINAL_ARTICLE
Proximity Point Properties for Admitting Center Maps
In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:C\rightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.
https://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf
2019-07-01
159
167
10.22130/scma.2018.79127.368
Admitting center map
Nonexpansive map
Cochebyshev set
Best proximity pair
Mohammad Hosein
Labbaf Ghasemi
mhlgh@yahoo.com
1
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.
AUTHOR
Mohammad Reza
Haddadi
haddadi@abru.ac.ir
2
Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
LEAD_AUTHOR
Noha
Eftekhari
eftekharinoha@yahoo.com
3
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.
AUTHOR
[1] A. Abkar and M. Gabeleh, Best proximity points of non-self mappings, Top, 21 (2013), pp. 287-295.
1
[2] R.P. Agarwal, E. Karapınar, D. O'Regan, and A.F. Roldán-López-de-Hierro, Fixed point theory in metric type spaces, Switzerland, Springer, 2015.
2
[3] R.P. Agarwal, D. O'Regan, and D.R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, New York, Springer, 2009.
3
[4] T.D. Benavides, J.G. Falset, E. Llorens-Fuster, and P.L. Ramírez, Fixed point properties and proximinality in Banach spaces, Nonlinear Anal., 71 (2009), pp. 1562-1571.
4
[5] X.P. Ding and K.K. Tan, On equilibria of non-compact generalized games, J. Math. Anal. Appl., 177 (1993), pp. 226-238.
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[6] W.G. Dotson, On the Mann iterative process, Trans. Amer. Math. Soc., 149 (1970), pp. 65-73.
6
[7] A.A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), pp. 1001-1006.
7
[8] J. Garcia-Falset, E. Llorens-Fuster, and S. Prus, The fixed point property for mappings admitting a center, Nonlinear Anal., 66 (2007), pp. 1257-1274.
8
[9] M.R. Haddadi and S.M. Moshtaghioun, Some results on the best proximity pair, Abstract and Applied Analysism, 2011 (2011).
9
[10] W.K. Kim and S. Kum, Best proximity pairs and Nash equilibrium pairs, J. Korean Math. Soc., 45 (2008), pp. 1297-1310.
10
[11] W. Kirk and N. Shahzad, Fixed point theory in distance spaces, Springer, 2016.
11
[12] T.D. Narang, On best coapproximation in normed linear spaces, Rocky Mountain J. Math., 1 (1992), pp. 265-287.
12
[13] H.K. Nashine, P. Kumam, and C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 2013 (2013), pp. 2-11.
13
[14] V.S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), pp. 4804-4808.
14
[15] J. Zhang, Y. Su, and Q. Cheng, Best proximity point theorems for generalized contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), pp. 1-7.
15
ORIGINAL_ARTICLE
Some Properties of Continuous $K$-frames in Hilbert Spaces
The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The $K$-frames were introduced by G$\breve{\mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of $K$-frames, there are many differences between $K$-frames and standard frames. $K$-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous $K$-frames or briefly c$K$-frames, namely some operators preserving and some identities for c$K$-frames. Also, the stability of these frames are discussed.
https://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf
2019-07-01
169
187
10.22130/scma.2018.85866.432
$K$-frame
c-frame
c$K$-frame
Local c$K$-atoms
Gholamreza
Rahimlou
grahimlou@gmail.com
1
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
AUTHOR
Reza
Ahmadi
rahmadi@tabrizu.ac.ir
2
Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
LEAD_AUTHOR
Mohammad Ali
Jafarizadeh
jafarizadeh@tabrizu.ac.ir
3
Faculty of Physic, University of Tabriz, Tabriz, Iran.
AUTHOR
Susan
Nami
s.nami@tabrizu.ac.ir
4
Faculty of Physic, University of Tabriz, Tabriz, Iran.
AUTHOR
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14
ORIGINAL_ARTICLE
A Proposed Preference Index For Ranking Fuzzy Numbers Based On $\alpha$-Optimistic Values
In this paper, we propose a novel method for ranking a set of fuzzy numbers. In this method a preference index is proposed based on $\alpha$-optimistic values of a fuzzy number. We propose a new ranking method by adopting a level of credit in the ordering procedure. Then, we investigate some desirable properties of the proposed ranking method.
https://scma.maragheh.ac.ir/article_35734_337333ac6c579e7a1e17797cdb481089.pdf
2019-07-01
189
201
10.22130/scma.2018.73477.303
$alpha$-Optimistic value
Fuzzy ranking
Preference index
Roboustness
Mehdi
Shams
mehdi_shams1357@yahoo.com
1
Department of Statistics, School of Mathematics, University of Kashan, Kashan,Iran.
LEAD_AUTHOR
Gholamreza
Hesamian
ghesamian@math.iut.ac.ir
2
Department of Mathematical Sciences, Payame Noor University, Tehran, Iran.
AUTHOR
[1] S. Abbasbandy, and B. Asady, Ranking of fuzzy numbers by sign distance, Inform. Sciences., 176 (2006), pp. 2405-24016.
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50
ORIGINAL_ARTICLE
Topological Centers and Factorization of Certain Module Actions
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $\pi_\ell: A\times X\rightarrow X$ and $\pi_r: X\times A\rightarrow X$, respectively. In this paper, we study the topological centers of the left module action $\pi_{\ell_n}: A\times X^{(n)}\rightarrow X^{(n)}$ and the right module action $\pi_{r_n}:X^{(n)}\times A\rightarrow X^{(n)}$, which inherit from the module actions $\pi_\ell$ and $\pi_r$, and also the topological centers of their adjoints, from the factorization property point of view, and then, we investigate conditions under which these bilinear maps are Arens regular or strongly Arens irregular.
https://scma.maragheh.ac.ir/article_35723_a8368ffd978c33879a6cf9ae4f4947df.pdf
2019-07-01
203
215
10.22130/scma.2018.76242.344
Topological centers
Module actions
Arens regular
Strongly Arens irregular
Sedigheh
Barootkoob
s.barutkub@ub.ac.ir
1
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
LEAD_AUTHOR
[1] R. Arens, Operations induced in function classes, Monatsh. Math., 55 (1951), pp. 1-19.
1
[2] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2 (1951), pp 839-848.
2
[3] N. Arikan, Arens regularity and reflexivity, J. Math. oxford, 32 (1981), pp. 383-388.
3
[4] S. Barootkoob, S. Mohammadzadeh, and H.R.E. Vishki, Topological centers of certain Banach module actions, Bull. Iranian. Math. Soc., 35 (2009), pp. 25-36.
4
[5] S. Barootkoob, S. Mohammadzadeh, and H.R.E. Vishki, Erratum: Topological centers of certain Banach module actions, Bull. Iranian. Math. Soc., 36 (2010), pp. 273-274.
5
[6] M. Eshaghi Gordgi and M. Filali, Arens regularity of module actions, Studia Math., 181 (2007), pp. 237-254.
6
[7] K. Haghnejad Azar, Arens regularity of bilinear forms and unital Banach module spaces, Bull. Iranian Math. Soc., 40 (2014), pp. 505-520.
7
[8] V. Losert, M. Neufang, J. Pachl, and J. Stebranse, Proof of the Ghahramani-Lau conjecture, Adv. Math., 290 (2016), pp. 709-738.
8
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9