Solution and stability of a new reciprocal type functional equation

Abstract

The aim of this paper is to obtain the general solution of a reciprocal functional equation of the form
\begin{equation*}\frac{1}{f(x+u,y+v)}=\frac{1}{2f(2x+y,2u+v)}+\frac{1}{2f(y,v)}\end{equation*}
and investigate its generalized Hyers-Ulam stability.