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 Hyers-Ulam stability of the following functionalequation f (2x  y)  f (2x  y)  (n 1)(n  2)(n  3) f ( y)  2n2 f (x  y)  f (x  y)  6 f (x) where n  1,2,3,4 , in non–Archimedean spaces, by using direct and fixed point methods.