Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 812545, 24 pages
doi:10.1155/2010/812545
Research Article

A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

Tian Zhou Xu,1 John Michael Rassias,2 and Wan Xin Xu3

1Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China
2Sections of Mathematics and Informatics, Pedagogical Department E.E., National and Capodistrian University of Athens, 4, Agamemnonos Str., Aghia Paraskevi, 15342 Athens, Greece
3School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 28 June 2010; Accepted 2 September 2010

Academic Editor: Xue Zhong He

Copyright © 2010 Tian Zhou Xu 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.

Abstract

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation f(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)+((k4−k2)/12)[f(2y)+f(−2y)−4f(y)−4f(−y)] for a fixed integer k with k≠0,±1 in non-Archimedean normed spaces.