Abstract
This paper is devoted to the study of hyperstability phenomena in the context of convex modular spaces. In particular, we investigate the hyperstability of three fundamental functional equations: the quadratic equation
\begin{equation}
\varphi(x+y)+\varphi(x-y)=2\varphi(x)+2\varphi(y)
\end{equation}
the general linear equation
\begin{equation}
\varphi(ax+by)=A\varphi(x)+B\varphi(y)+C
\end{equation}
and the $n$-dimensional quadratic equation
\begin{equation} 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}
Using the direct method, we establish sufficient conditions under which every approximate solution of these equations in modular spaces coincides exactly with an exact solution. Our results extend earlier contributions obtained in Banach spaces via fixed point techniques, and provide new insights into the stability of functional equations in the broader context of modular spaces.
Key words: Hyers-Ulam stability; quadratic functional equation; general linear functional equation; hyperstability.
Full Text
Article Information
| Title | Hyperstability of some functional equations in modular spaces |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 4, 310-324 |
| DOI | 10.31392/MFAT-npu26_4.2025.02 |
| Milestones | Received 04/03/2025; Revised 30/08/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Abderrahman Baza
Laboratory Analysis, Geometry and Applications, Ibn Tofail University, Kenitra, Morocco
Mohamed Rossafi
Laboratory Analysis, Geometry and Applications, Higher School of Education and Training, Ibn Tofail University, Kenitra, Morocco
Mohammed Mouniane
Laboratory Analysis, Geometry and Applications, Higher School of Education and Training, Ibn Tofail University, Kenitra, Morocco
Citation Example
Abderrahman Baza, Mohamed Rossafi, and Mohammed Mouniane, Hyperstability of some functional equations in modular spaces, Methods Funct. Anal. Topology 31
(2025), no. 4, 310-324.
BibTex
@article {MFAT2140,
AUTHOR = {Abderrahman Baza and Mohamed Rossafi and Mohammed Mouniane},
TITLE = {Hyperstability of some functional equations in modular spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {4},
PAGES = {310-324},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_4.2025.02},
URL = {https://mfat.imath.kiev.ua/article/?id=2140},
}
