Direct and fixed point methods approach to the generalized Hyers-Ulam stability for a functional equation having monomials as solutions

Abstract

The main goal of this paper is the study of the generalized Hwyers-Ulam stability of the following functional equation f (2x + y) + f (2x - y) +(n - 1)(n - 2)(n -3)f (y) = 2(n-2)[f (x + y) + f (x - y) + 6f (x)] where n =1,2,3,4, in non-Archimedean spaces, by using direct and fixed point methods.