The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

Abstract

Lee, An and Park introduced the quadraticfunctional equation $f\left(2x+y\right)+f\left(2x-y\right)=8f\left(x\right)+2f\left(y\right)$ and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadraticfunctional equation in Banach spaces.