A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

Abstract

Copyright (C) 2010 Jung Rye Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f (x + 2y) + f (x-2y) = 4f(x + y) +4f(x-y) - 6f (x) + f (2y) + f(-2y) -4f (y) - 4f(-y) in Banach spaces.