Generalized Hyers-Ulam stability of a quadratic functional equation in (β,p)-Banach spaces

Abstract

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability of the following quadratic functional equation

f(ax+y)+a/2[f(x−y)+ f(y−x)] = a(a+1)f(x)+(a+1)f(y)

in (β,p)-Banach spaces, where a is a nonzero fixed integer such that a≠0,−1,−2.