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

Abstract

The aim of this paper is to obtain the general solution of a reciprocal functional equation of the form
\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*}
and investigate its  generalized Hyers-Ulam-Rassias stability.