A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces

Abstract

Using direct method, Kenary (Acta Universitatis Apulensis, to appear) proved the Hyers-Ulam stability of the following functional equation f(mx+ny)=(m+n)f(x+y)/2 + (m-n)f(x-y)/2 in non-Archimedean normed spaces and in random normed spaces, where m, n are different integers greater than 1. In this article, using fixed point method, we prove the Hyers-Ulam stability of the above functional equation in various normed spaces.