Difference and functional equations
1. 2-Banach stability results for the radical cubic functional equation related to quadratic mapping

R. E. Ghali; S. Kabbaj

Volume 09, Issue 01 , Winter 2020, , Pages 35-51

Abstract
  The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$f\left(\sqrt[3]{ax^{3}+by^{3}}\right)+f\left(\sqrt[3]{ax^{3}-by^{3}}\right)=2a^{2}f(x)+2b^{2}f(y),\;\; x,y\in\mathbb{R},$$for a mapping $f$ from $\mathbb{R}$ ...  Read More

Functional analysis
2. Operator frame for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$

M. Rossafi; S. Kabbaj

Volume 08, Issue 02 , Spring 2019, , Pages 85-95

Abstract
  ‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ...  Read More

Fixed point theory
3. Generalized hyperstability of the cubic functional equation in ultrametric spaces

Y. ‎Aribou; H. Dimou; S. Kabbaj

Volume 08, Issue 02 , Spring 2019, , Pages 97-104

Abstract
  ‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.  Read More

Functional analysis
4. A new type of Hyers-Ulam-Rassias stability for Drygas functional equation

M. Sirouni; M. ‎Almahalebi; S. ‎Kabbaj

Volume 07, Issue 04 , Autumn 2018, , Pages 251-260

Abstract
  In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brz\c{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements ...  Read More

Functional analysis
5. $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules

M. Rossafi; S. Kabbaj

Volume 07, Issue 01 , Winter 2018, , Pages 63-71

Abstract
  In this paper, we introduce the concepts of $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules and we establish some results.  Read More