On the stability of radical functional equation in modular space

TL;DR

This paper investigates the stability of a specific radical functional equation within modular spaces, establishing generalized Hyer Ulam stability using direct methods and fixed point theorems.

Contribution

It extends the stability analysis of a radical functional equation to modular spaces, providing new results on its Hyer Ulam stability for odd integers s ≥ 3.

Findings

Proves Hyer Ulam stability of the functional equation in modular spaces.

Utilizes direct method and fixed point theorem for the proof.

Establishes stability results for |q| ≤ 1 and odd integer s ≥ 3.

Abstract

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 $s$ is an odd integer such that $s\geq 3$, in modular space, using the direct method, and the fixed point theorem.