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Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} \phi(x+y, z+w)+\phi(x-y, z-w)-2 \phi(x, z)-2 \phi(x, w)=0 \end{equation} in modular space satisfying the Fatou…

General Mathematics · Mathematics 2024-06-25 Abderrahman Baza , Mohamed Rossafi , Choonkil Park

In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equation $$ (E):\;\;\;\; f(xy)+\chi(y)f(\sigma(y)x)=2f(x)g(y),\; x,y\in G,$$ where $G$ is a group, $\sigma$ is an involutive…

Classical Analysis and ODEs · Mathematics 2015-05-26 Elqorachi Elhoucien , Redouani Ahmed

Using fixed point methods, we prove the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen--type functional equation…

Functional Analysis · Mathematics 2009-12-21 A. Ebadian , Sh. Najafzadeh

In this paper, by using the orthogonally fixed point method, we prove the Hyers-Ulam stability and the hyperstability of orthogonally 3-Lie homomorphisms for additive $\rho$-functional equation in 3-Lie algebras.\\ Indeed, we investigate…

Functional Analysis · Mathematics 2020-02-18 Vahid Keshavarz , Sedigheh Jahedi , Themistocles M. Rassias

In this work, we prove the generalised Hyer Ulam stability of the following functional equation \begin{equation}\label{Eq-1} \phi(x)+\phi(y)+\phi(z)=q \phi\left(\sqrt[s]{\frac{x^s+y^s+z^s}{q}}\right),\qquad |q| \leq 1 \end{equation} and $s$…

Functional Analysis · Mathematics 2024-08-21 Abderrahman Baza , Mohamed Rossafi

This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating…

Functional Analysis · Mathematics 2025-08-15 Jing Zhang , Qi Liu , Yongmo Hu , Linlin Fu , Yuxin Wang , Jinyu Xia , John Michael Rassias , Choonkil Park , Yongjin Li

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and…

Functional Analysis · Mathematics 2021-07-23 Soon-Mo Jung , Mohammad Sal Moslehian , Prasanna K. Sahoo

In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

Commutative Algebra · Mathematics 2018-10-25 Ajebbar Omar , Elqorachi Elhoucien , Themistocles M. Rassias

The stability problem in Ulam's sense has recently been explored in locally convex cone environments, as shown in \cite{ MNF, NR1, NR2}. In continuation of this research direction, our work examines the stability properties of the quadratic…

Functional Analysis · Mathematics 2025-08-19 J. -H. Bae , J. Mohammadpour , A. Najati

In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.

Functional Analysis · Mathematics 2015-12-16 Soon-Mo Jung , Dorian Popa , Michael Th. Rassias

In this paper, we investigate some hyperstability results, inspired by the concept of Ulam stability, for the following functional equations: \begin{equation} \varphi(x+y)+\varphi(x-y)=2\varphi(x)+2\varphi(y) \end{equation} \begin{equation}…

Functional Analysis · Mathematics 2024-10-15 Abderrahman Baza , Mohamed Rossafi , Mohammed Mouniane

In this paper, we establish the generalized Hyers--Ulam--Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation $r f(\frac{sx+ty}{r}) = s f(x) + t f(y)$.

Functional Analysis · Mathematics 2021-07-23 Mohammad Sal Moslehian , Laszlo Szekelyhidi

Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$\frac{1}{\mid K\mid}\sum_{k\in K}f(x+k\cdot y)=g(x)+h(y),\;\;x,y\in E$$ from a normed space $E$ into a complete…

Functional Analysis · Mathematics 2014-06-17 E. Elqorachi , John M. Rassias , B. Bouikhalene

In this paper, we investigate homomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras, associated with the following functional equation…

Operator Algebras · Mathematics 2008-12-17 M. Bavand Savadkouhi , M. Eshaghi Gordji , N. Ghobadipour

In this paper, we establish the generalized Hyers--Ulam--Rassias stability of $C^*$-ternary ring homomorphisms associated to the Trif functional equation \begin{eqnarray*} d \cdot C_{d-2}^{l-2} f(\frac{x_1+... +x_d}{d})+…

Functional Analysis · Mathematics 2008-04-30 Mohammad Sal Moslehian

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach…

Functional Analysis · Mathematics 2021-07-23 M. Mirzavaziri , M. S. Moslehian

In this paper, we give a proof of the Hyers-Ulam stability of the Jensen functional equation $$f(xy)+f(x\sigma(y))=2f(x),\phantom{+} x,y\in{G},$$ where $G$ is an amenable semigroup and $\sigma$ is an involution of $G.$

Functional Analysis · Mathematics 2014-06-17 Bouikhalene Belaid , Elqorachi Elhoucien

We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized…

Functional Analysis · Mathematics 2015-10-08 Maysam Maysami Sadr

In this paper we establish the stability of the functional equation \begin{equation*}f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y),\;x,y\in G,\end{equation*} where $G$ is an amenable group.

Rings and Algebras · Mathematics 2018-09-20 Ajebbar Omar , Elqorachi Elhoucien

In this paper, we present a study on the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.

Classical Analysis and ODEs · Mathematics 2018-07-18 J. Vanterler da C. Sousa , E. Capelas de Oliveira , F. G. Rodrigues