Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
Mohammad
Mahmoudieh
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
author
Hessam
Hosseinnezhad
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
author
Gholamreza
Abbaspour Tabadkan
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
1
18
https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf
dx.doi.org/10.22130/scma.2018.77908.356
A Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type
Shahram
Banaei
Department of Mathematics, Bonab Branch, Islamic Azad University, Bonab, Iran.
author
Mohammad Bagher
Ghaemi
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
19
35
https://scma.maragheh.ac.ir/article_34954_fb1f8292e46d2d8e27e2ad9e34eb5f31.pdf
dx.doi.org/10.22130/scma.2018.74869.322
Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces
Yahya
Alizadeh
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.
author
Mohammad Reza
Abdollahpour
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
37
48
https://scma.maragheh.ac.ir/article_34963_35384b34dcf883a65808ec86a7f3b34c.pdf
dx.doi.org/10.22130/scma.2019.68582.264
Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
Zahra
Kalateh Bojdi
Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.
author
Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.
author
Ali
Tavakoli
Mathematics department, University of Mazandaran, Babolsar, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
49
63
https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf
dx.doi.org/10.22130/scma.2018.74791.321
Theory of Hybrid Fractional Differential Equations with Complex Order
Devaraj
Vivek
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
author
Omid
Baghani
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
author
Kuppusamy
Kanagarajan
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
65
76
https://scma.maragheh.ac.ir/article_34967_a19fd276ba6778bbb6bed7f43599acca.pdf
dx.doi.org/10.22130/scma.2018.72907.295
$\sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras
Zahra
Hasanzadeh
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
author
Amin
Mahmoodi
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
77
89
https://scma.maragheh.ac.ir/article_34969_62c81b96df381db750dd155bb9dd2dbb.pdf
dx.doi.org/10.22130/scma.2018.73939.308
Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces
Mohammad Esmael
Samei
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, 6517838695, Hamedan, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
91
106
https://scma.maragheh.ac.ir/article_35070_810d28ad9c75d6e7f96342191446473e.pdf
dx.doi.org/10.22130/scma.2018.72350.288
Bounded Approximate Character Amenability of Banach Algebras
Hasan
Pourmahmood Aghababa
Department of Mathematics, University of Tabriz, Tabriz, Iran.
author
Fourogh
Khedri
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
author
Mohammad Hossein
Sattari
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
107
118
https://scma.maragheh.ac.ir/article_35435_9d883ba7e3298bfb19d2cc5f830fe1a2.pdf
dx.doi.org/10.22130/scma.2018.79315.372
Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Kobra
Esmaeili
Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
119
133
https://scma.maragheh.ac.ir/article_35724_a056298520b5f4f883e2417d01c90dcb.pdf
dx.doi.org/10.22130/scma.2018.78754.365
Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^\ast-$modules
Morteza
Mirzaee Azandaryani
Department of Mathematics, University of Qom, Qom, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
135
146
https://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf
dx.doi.org/10.22130/scma.2018.81624.396
Primitive Ideal Space of Ultragraph $C^*$-algebras
Mostafa
Imanfar
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
author
Abdolrasoul
Pourabbas
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
author
Hossein
Larki
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
147
158
https://scma.maragheh.ac.ir/article_35729_73ba5420990970a0ddcac2ce5d817221.pdf
dx.doi.org/10.22130/scma.2018.82725.404
Proximity Point Properties for Admitting Center Maps
Mohammad Hosein
Labbaf Ghasemi
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.
author
Mohammad Reza
Haddadi
Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
author
Noha
Eftekhari
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
159
167
https://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf
dx.doi.org/10.22130/scma.2018.79127.368
Some Properties of Continuous $K$-frames in Hilbert Spaces
Gholamreza
Rahimlou
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
author
Reza
Ahmadi
Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
author
Mohammad Ali
Jafarizadeh
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
author
Susan
Nami
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
169
187
https://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf
dx.doi.org/10.22130/scma.2018.85866.432
A Proposed Preference Index For Ranking Fuzzy Numbers Based On $\alpha$-Optimistic Values
Mehdi
Shams
Department of Statistics, School of Mathematics, University of Kashan, Kashan,Iran.
author
Gholamreza
Hesamian
Department of Mathematical Sciences, Payame Noor University, Tehran, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
189
201
https://scma.maragheh.ac.ir/article_35734_337333ac6c579e7a1e17797cdb481089.pdf
dx.doi.org/10.22130/scma.2018.73477.303
Topological Centers and Factorization of Certain Module Actions
Sedigheh
Barootkoob
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
author
text
article
2019
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
15
v.
1
no.
2019
203
215
https://scma.maragheh.ac.ir/article_35723_a8368ffd978c33879a6cf9ae4f4947df.pdf
dx.doi.org/10.22130/scma.2018.76242.344