Stability of a new generalized reciprocal type functional equation

TL;DR

This paper studies the stability of a complex reciprocal type functional equation, extending Hyers-Ulam stability concepts to both real and non-Archimedean spaces.

Contribution

It introduces the generalized Hyers-Ulam stability for a new reciprocal functional equation in diverse mathematical spaces.

Findings

Established stability conditions in real spaces.

Extended stability results to non-Archimedean spaces.

Provided bounds for approximate solutions.

Abstract

In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal type functional equation \begin{equation*}f(2x+y)+f(2x-y)=\frac{2f(x)f(y)\displaystyle{\sum_{\substack{k=0\\ \text{$k$ is even}}}^{ l}2^{l-k}\binom{l}{k}f(x)^{\frac{k}{l}}f(y)^{\frac{l-k}{l}}}}{\left(4f(y)^{\frac{2}{l}}-f(x)^{\frac{2}{l}}\right)^l}\end{equation*} in non-zero real and non-Archimedean spaces.