Hyers-Ulam-Rassias stability of a quadratic type functionalequation

Abstract

In this paper, we prove the stability of a quadratic type functional equation $$ \split & a^2 f\left({x+y+z}\over{a}\right)+a^2 f\left({x-y+z}\over{a}\right) +a^2f\left({x+y-z}\over{a}\right) \\ & +a^2f\left({-x+y+z}\over{a}\right)=4f(x)+4f(y)+4f(z). \endsplit $$