2021-10-21T00:08:47Z
https://scma.maragheh.ac.ir/?_action=export&rf=summon&issue=5734
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
Mohammad
Mahmoudieh
Hessam
Hosseinnezhad
Gholamreza
Abbaspour Tabadkan
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.
Multi-frame vector
Wandering vector
Local commutant
Unitary system
2019
07
01
1
18
https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
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
Mohammad Bagher
Ghaemi
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.
Measure of noncompactness
Fixed point theorem
Integral equations
2019
07
01
19
35
https://scma.maragheh.ac.ir/article_34954_fb1f8292e46d2d8e27e2ad9e34eb5f31.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces
Yahya
Alizadeh
Mohammad Reza
Abdollahpour
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.
Controlled continuous $g$-frames
$(mathcal{C}
mathcal{C}')$-controlled continuous $g$-Bessel families
Multiplier of continuous $g$-frames
2019
07
01
37
48
https://scma.maragheh.ac.ir/article_34963_35384b34dcf883a65808ec86a7f3b34c.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
Zahra
Kalateh Bojdi
Ataollah
Askari Hemmat
Ali
Tavakoli
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.
MRA
Heat equation
wavelet method
Finite difference
2019
07
01
49
63
https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Theory of Hybrid Fractional Differential Equations with Complex Order
Devaraj
Vivek
Omid
Baghani
Kuppusamy
Kanagarajan
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.
Hybrid fractional differential equations
Initial value problem
Complex order
Dhage's fixed point theorems
Existence of mild solution
2019
07
01
65
76
https://scma.maragheh.ac.ir/article_34967_a19fd276ba6778bbb6bed7f43599acca.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
$sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras
Zahra
Hasanzadeh
Amin
Mahmoodi
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.
$sigma$-Connes amenability
Pseudo-amenability
Pseudo-Connes amenability
Beurling algebras
2019
07
01
77
89
https://scma.maragheh.ac.ir/article_34969_62c81b96df381db750dd155bb9dd2dbb.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces
Mohammad Esmael
Samei
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.
Inexact iterative
Fixed point
Contraction multifunction
Hausdorff fuzzy metric
2019
07
01
91
106
https://scma.maragheh.ac.ir/article_35070_810d28ad9c75d6e7f96342191446473e.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Bounded Approximate Character Amenability of Banach Algebras
Hasan
Pourmahmood Aghababa
Fourogh
Khedri
Mohammad Hossein
Sattari
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.
Banach algebras
Bounded approximate character amenability
Bounded approximate character contractibility
Locally compact groups
2019
07
01
107
118
https://scma.maragheh.ac.ir/article_35435_9d883ba7e3298bfb19d2cc5f830fe1a2.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Kobra
Esmaeili
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.
Essential norms
Generalized weighted composition operators
Logarithmic Bloch type spaces
$N$th weighted type spaces
2019
07
01
119
133
https://scma.maragheh.ac.ir/article_35724_a056298520b5f4f883e2417d01c90dcb.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules
Morteza
Mirzaee Azandaryani
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.
Frame
$g$-frame
Fusion frame
Biorthogonal sequence
Approximate duality
2019
07
01
135
146
https://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Primitive Ideal Space of Ultragraph $C^*$-algebras
Mostafa
Imanfar
Abdolrasoul
Pourabbas
Hossein
Larki
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.
Ultragraph
Ultragraph $C^*$-algebra
Primitive ideal
2019
07
01
147
158
https://scma.maragheh.ac.ir/article_35729_73ba5420990970a0ddcac2ce5d817221.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Proximity Point Properties for Admitting Center Maps
Mohammad Hosein
Labbaf Ghasemi
Mohammad Reza
Haddadi
Noha
Eftekhari
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.
Admitting center map
Nonexpansive map
Cochebyshev set
Best proximity pair
2019
07
01
159
167
https://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Some Properties of Continuous $K$-frames in Hilbert Spaces
Gholamreza
Rahimlou
Reza
Ahmadi
Mohammad Ali
Jafarizadeh
Susan
Nami
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.
$K$-frame
c-frame
c$K$-frame
Local c$K$-atoms
2019
07
01
169
187
https://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
A Proposed Preference Index For Ranking Fuzzy Numbers Based On $alpha$-Optimistic Values
Mehdi
Shams
Gholamreza
Hesamian
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.
$alpha$-Optimistic value
Fuzzy ranking
Preference index
Roboustness
2019
07
01
189
201
https://scma.maragheh.ac.ir/article_35734_337333ac6c579e7a1e17797cdb481089.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2019
15
1
Topological Centers and Factorization of Certain Module Actions
Sedigheh
Barootkoob
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.
Topological centers
Module actions
Arens regular
Strongly Arens irregular
2019
07
01
203
215
https://scma.maragheh.ac.ir/article_35723_a8368ffd978c33879a6cf9ae4f4947df.pdf