Stability of a mixed type additive, quadratic, cubic and quartic functional equation

Abstract

We find the general solution of the functional equation (Formula presented)in the context of linear spaces. We prove that if a mapping f from a linear space X into a Banach space Y satisfies f (0) = 0 and (Formula presented) where ε > 0, then there exist a unique additive mapping A: X → Y, a unique quadratic mapping Q1: X → Y, a unique cubic mapping C: X → Y and a unique quartic mapping Q2: X → Y such that.