FIXED POINTS AND HYERS-ULAM-RASSIAS STABILITY OF THE QUADRATIC AND JENSEN FUNCTIONAL EQUATIONS

Abstract

In this paper, we apply a fixed point theorem to the proof of Hyers-Ulam-Rassias stability property for the quadratic functional equation

\frac{1}{|K|} \sum_{k \in K} f(x + k . y) = f(x) + f(y), x, y \in E_1

and for the Jensen functional equation

\frac{1}{|K|} \sum_{k \in K} f(x + k . y) = f(x), x, y \in E_1

from a normed space E_1 into a quasi Banach space E_2, where K is a finite cyclic transformation group of E_1.