Further stability results of the functional equation $f(2x+y)+f\left(\frac{x+y}{2}\right) =\frac{2f(x)f(y)}{f(x)+f(y)}+\frac{2f(x+y)f(y-x)}{3f(y-x)-f(x+y)}$

TL;DR

This paper explores the stability of a complex reciprocal functional equation within non-Archimedean spaces, extending previous results and employing a direct method for analysis.

Contribution

It provides new stability results for a generalized reciprocal functional equation in non-Archimedean spaces, using a direct analytical approach.

Findings

Established stability conditions for the functional equation

Extended stability results to non-Archimedean spaces

Demonstrated the effectiveness of the direct method

Abstract

In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal functional equation \begin{equation*}f(2x+y)+f\left(\frac{x+y}{2}\right) =\frac{2f(x)f(y)}{f(x)+f(y)}+\frac{2f(x+y)f(y-x)}{3f(y-x)-f(x+y)}\end{equation*} in non-Archimedean space using a direct method.