A fixed point approach to the stability of an additive cubic functional equation in paranormed spaces

Abstract

In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of the additive cubic functional equation

f(x-ky)=k²[f(x+y)+ f(x-y)]+2(1- k²)f(x)

for fixed integers k, with k≠0,±1 in paranormed spaces.