The Hyers–Ulam stability of an additive-quadratic s-functional inequality in Banach spaces

Abstract

For any fixed s∈{z∈C:z≠0and|z|<1}, we consider the following functional inequality: ‖f(a+a′,c+c′)+f(a+a′,c-c′)+f(a-a′,c+c′)+f(a-a′,c-c′)-4f(a,c)-4f(a,c′)‖≤‖s(2f(a+a′,c-c′)+2f(a-a′,c+c′)-4f(a,c)-4f(a,c′)+4f(a′,c′))‖.In this paper, we obtain the Hyers–Ulam stability of the proposed functional inequality using the direct and fixed point methods.