Fixed Points and Stability of a Generalized Quadratic Functional Equation

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the generalized quadratic functional equation f(rx+sy)=r2f(x)+s2f(y)+(rs/2)[f(x+y)−f(x−y)] in Banach modules, where r,s are nonzero rational numbers with r2+s2≠1.