##### Volume 01 (2012)
Functional analysis
##### On the h-Jensen's operator inequality

S. S. Hashemi Karouei; M. S. Asgari; M. Shah Hosseini; N. Ghafoori Adl

Articles in Press, Accepted Manuscript, Available Online from 16 April 2022
##### Abstract
‎In this paper‎, ‎we prove Jensen's operator inequality for an h-convex function and we point out the results for classes of continuous‎ ‎fields of operators‎. ‎Also‎, ‎some generalizations of Jensen's operator inequality and some properties of the h-convex function ...  Read More

Operator theory
##### On equality of complete positivity and complete copositivity of positive map

C. A. Winda; N. B. Okelo; O. Ongati

Articles in Press, Corrected Proof, Available Online from 07 June 2022
##### Abstract
‎In this paper we construct a $2$-positive map from $\ma_4(\Complex)$ to $\ma_5(\Complex)$ and state the conditions under which the map is positive and completely positive (copositivity of positive)‎. ‎The construction allows us to create a decomposable map, where the Choi matrix of complete ...  Read More

Operator theory
##### Equivariant homologies for operator algebras; a survey

A. Shirinkalam

Articles in Press, Corrected Proof, Available Online from 30 June 2022
##### Abstract
‎This is a survey of a variety of equivariant (co)homology theories for operator algebras‎. ‎We briefly discuss a background on equivariant Hochschild cohomology‎. ‎We discuss a notion of equivariant $L^2$-cohomology and equivariant $L^2$-Betti numbers for subalgebras of a von ...  Read More

Operator theory
##### Reverses of the first Hermite-Hadamard type inequality for the square operator modulus in Hilbert spaces

S. S. Dragomir

Volume 11, Issue 01 , March 2022, , Pages 1-13
##### Abstract
‎Let $\left( H;\left\langle \cdot‎ ,‎\cdot \right\rangle \right)$ be a complex‎ ‎Hilbert space‎. ‎Denote by $\mathcal{B}\left( H\right)$ the Banach $C^{\ast }$-‎algebra of bounded linear operators on $H$‎. ‎For $A\in \mathcal{B}\left(‎H\right)$ we define the ...  Read More

Functional analysis
##### Atomic systems in $n$-Hilbert spaces and their tensor products

P. Ghosh; T. K. Samanta

Volume 10, Issue 04 , December 2021, , Pages 241-256

##### Abstract
Concept of a family of local atoms in $n$-Hilbert space is being studied. $K$-frame in tensor product of $n$-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of $n$-Hilbert spaces is presented and established a relationship between atomic systems in $n$-Hilbert ...  Read More

Functional analysis
##### Convergence, stability and data dependence results for contraction and nonexpansive mappings by a new four step algorithm

U. E. Udofia; D. Igbokwe

Volume 10, Issue 04 , December 2021, , Pages 295-321

##### Abstract
Here we show that the UI-iteration scheme (Udofia and Igbokwe, [24]) can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the ...  Read More

Operator theory
##### A closure operator versus purity

M. Ghorbani

Volume 10, Issue 03 , September 2021, , Pages 199-203

##### Abstract
‎Any notion of purity is normally defined in terms of‎ ‎solvability of some set of equations‎. ‎To study mathematical notions‎, ‎such as injectivity‎, ‎tensor products‎, ‎flatness‎, ‎one needs to have some categorical and‎ ‎algebraic ...  Read More

Operator theory
##### Construction of frame relative to $n$-Hilbert space

P. Ghosh; T. K. Samanta

Volume 10, Issue 02 , June 2021, , Pages 117-130

##### Abstract
In this paper, our aim is to introduce the concept of a frame in $n$-Hilbert space and describe some of its properties. We further discuss tight frame relative to $n$-Hilbert space. At the end, we study the relationship between frame and bounded linear operator in $n$-Hilbert space.  Read More

Operator theory
##### Coupled fixed point results for $T$-contractions on $\mathcal{F}$-metric spaces and an application

Volume 10, Issue 01 , March 2021, , Pages 1-10

##### Abstract
The main purpose of this article is to introduce the concept of $T$-contraction type mappings in the function weighed metric spaces and to obtain some coupled fixed points theorems in this framework. Also, an example and an application of the existence of a solution of a system of nonlinear integral ...  Read More

Functional analysis
##### A new implicit iteration process for approximating common fixed points of $\alpha$-demicontraction semigroup

A. E. Ofem; D. I. Igbokwe

Volume 10, Issue 01 , March 2021, , Pages 19-34

##### Abstract
It is our purpose in this paper to introduce the concept of $\alpha$-demicontractive semigroup. Also, we construct a new implicit iterative scheme for approximating the common fixed points of $\alpha$-demicontractive semigroup. We prove strong convergence of our new iterative scheme to the common fixed ...  Read More

Operator theory
##### Integral type contraction and coupled fixed point theorems in ordered G-metric spaces

E. Lotfali Ghasab; H. Majani; G. Soleimani Rad

Volume 09, Issue 02 , June 2020, , Pages 113-120

##### Abstract
In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.  Read More

Operator theory
##### $C$-class functions on common fixed point theorems for weak‎ ‎contraction mapping of integral type in modular spaces

H. A. Hammad; R. A. Rashwan; A. H. Ansari

Volume 08, Issue 04 , December 2019, , Pages 265-285

##### Abstract
‎In this paper‎, ‎we use the concept of $C$-class functions introduced‎ ‎by Ansari [4] to prove the existence and uniqueness of‎ ‎common fixed point for self-mappings in modular spaces of integral‎ ‎inequality‎. ‎Our results extended and generalized ...  Read More

Linear and multilinear algebra; matrix theory
##### *-frames in Hilbert modules over pro-C*-algebras

M. Naroei Irani; A. Nazari

Volume 08, Issue 01 , February 2019, , Pages 1-10

##### Abstract
‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$C^*$-modules‎. ‎We investigate the relations between frames and $\ast$-frames‎. ‎Some properties of $\ast$-frames in Hilbert pro-$C^*$-modules ...  Read More

Functional analysis
##### System of AQC functional equations in non-Archimedean normed spaces

H. Majani

Volume 08, Issue 01 , February 2019, , Pages 41-52

##### Abstract
‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems ...  Read More

Operator theory
##### Algebraic distance in algebraic cone metric spaces and its properties

Volume 07, Issue 04 , November 2018, , Pages 273-280

##### Abstract
In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.  Read More

Difference and functional equations
##### Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras

R. Gholami; Gh. Askari; M. Eshaghi Gordji

Volume 07, Issue 02 , June 2018, , Pages 109-119

##### Abstract
In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring ...  Read More

Operator theory
##### Characterization of $(\delta‎, ‎\varepsilon)$-double derivation on rings ‎and ‎algebras

Z. Jokar; A. Niknam

Volume 06, Issue 03 , September 2017, , Pages 191-198

##### Abstract
This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $\mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, \delta, \varepsilon$ are additive mappings satisfying$$d(x^n) = \sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+\sum^{n-1}_{j=1}\sum^{j}_{i=1}x^{n-1-j}\Big(\delta(x)x^{j-i}\varepsilon(x)+\varepsilon(x)x^{j-i}\delta(x)\Big)x^{i-1}\quad$$for ...  Read More

Functional analysis
##### Duals and approximate duals of g-frames in Hilbert spaces

M. Mirzaee Azandaryani; A. Khosravi

Volume 04, Issue 04 , December 2015, , Pages 259-265

##### Abstract
In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We ...  Read More

Functional analysis
##### New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

F. Aboutorabi Goudarzi; M. S. Asgari

Volume 04, Issue 02 , May 2015, , Pages 131-142

##### Abstract
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion ...  Read More

Operator theory
##### On the boundedness of almost multipliers on certain Banach algebras

E. Ansari-Piri; M. Shams Yousefi; S. Nouri

Volume 04, Issue 02 , May 2015, , Pages 143-152

##### Abstract
Almost multiplier is rather a new concept in the theory of almost functions. In this paper we discussion the boundedness of almost multipliers on some special Banach algebras, namely stable algebras. We also define an adjoint and extension for almost multiplier.  Read More

Operator theory
##### On dual shearlet frames

M. Amin khah; A. Askari Hemmat; R. Raisi Tousi

Volume 04, Issue 02 , May 2015, , Pages 159-163

##### Abstract
In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.  Read More

Functional analysis
##### Frames for compressed sensing using coherence

L. Gavruta; G. Zamani Eskandani; P. Gavruta

Volume 04, Issue 01 , February 2015, , Pages 25-34

##### Abstract
We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied. Moreover, we give better estimations then the ones given ...  Read More

Functional analysis
##### The solutions to some operator equations in Hilbert $C^*$-module

Volume 04, Issue 01 , February 2015, , Pages 35-42

##### Abstract
In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, ...  Read More

Functional analysis
##### On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

M. Rashidi-Kouchi

Volume 04, Issue 01 , February 2015, , Pages 53-63

##### Abstract
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. ...  Read More

Group theory
##### Module amenability and module biprojectivity of θ-Lau product of Banach algebras

D. Ebrahimi Bagha; H. Azaraien

Volume 03, Issue 03 , September 2014, , Pages 185-196

##### Abstract
In this paper we study the relation between module amenability of $\theta$-Lau product $A×_\theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×\theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_\theta l^1(S)$ is module ...  Read More