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

摘要

The main goal of this paper is the study of the generalized Hyers-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.