ON THE HYERS-ULAM-RASSIAS STABILITY OF THE FUNCTIONAL EQUATION

Abstract

In this paper, we establish the Hyers-Ulam-Rassias stability of the functional equation f(px2 + y2) = f(x)+f(y). The generalized Hyers-Ulam stability originated from the Rassias's stability theorem that appeared in the paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].