Hyperstability of some functional equations in modular spaces
Functional Analysis
2024-10-15 v1
Abstract
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} \varphi(ax+by) = A\varphi(x)+B\varphi(y)+C \end{equation} \begin{equation}\label{eqnd} f\left(\sum_{i=1}^{m}x_{i}\right)+\sum_{1\leq i<j\leq m}f\big(x_{i}-x_{j}\big)=m\sum_{i=1}^{m}f(x_{i}) \end{equation} in modular spaces.
Cite
@article{arxiv.2410.09082,
title = {Hyperstability of some functional equations in modular spaces},
author = {Abderrahman Baza and Mohamed Rossafi and Mohammed Mouniane},
journal= {arXiv preprint arXiv:2410.09082},
year = {2024}
}