Stability of the New Generalized Linear Functional Equation in Normed Spaces via the Fixed Point Method in Generalized Metric Spaces

Laddawan Aiemsomboon, Wutiphol Sintunavarat

Abstract

The aim of this paper is to apply the classical metric fixed point method for proving the Hyers-Ulam stability of the generalized linear functional equation of the form\begin{equation*}    2f(x+y)+f(x-y)+f(y-x)=2f(x)+2f(y), \end{equation*}for all $x,y \in X$, where $f$ maps from a Banach space $X$ into a Banach space $Y$.