Abstract
In this work, we prove the generalised Hyer Ulam stability of the following functional equation
\begin{equation}
\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 $s$ is an odd integer such that $s\geq 3$,
in modular space, using the direct method, and the fixed point theorem.
Key words: Modular spaces, Hyers-Ulam stability, Fatou property, $\Delta_2$-condition.
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Article Information
| Title | On the stability of radical functional equation in modular space |
| Source | Methods Funct. Anal. Topology, Vol. 30 (2024), no. 3-4, 108-116 |
| DOI | 10.31392/MFAT-npu26_3-4.2024.03 |
| Copyright | The Author(s) 2024 (CC BY-SA) |
Authors Information
Abderrahman Baza
Laboratory of Analysis, Geometry and Application, Departement of Mathematics, Ibn Tofail University, Kenitra, Morocco
Mohamed Rossafi
Higher School of Education and Training, Ibn Tofail University, Kenitra, Morocco
Citation Example
Abderrahman Baza and Mohamed Rossafi, On the stability of radical functional equation in modular space, Methods Funct. Anal. Topology 30
(2024), no. 3, 108-116.
BibTex
@article {MFAT2089,
AUTHOR = {Abderrahman Baza and Mohamed Rossafi},
TITLE = {On the stability of radical functional equation in modular space},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {30},
YEAR = {2024},
NUMBER = {3},
PAGES = {108-116},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_3-4.2024.03},
URL = {https://mfat.imath.kiev.ua/article/?id=2089},
}
