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

摘要

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.