Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 824257, 19 pages
http://dx.doi.org/10.1155/2012/824257
Research Article

Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping

Hassan Azadi Kenary,1 Themistocles M. Rassias,2 H. Rezaei,1 S. Talebzadeh,3 and Won-Gil Park4

1Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran
2Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece
3Department of Mathematics, Islamic Azad University, Firoozabad Branch, Firoozabad, Iran
4Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of Korea

Received 10 October 2011; Accepted 23 December 2011

Academic Editor: Seenith Sivasundaram

Copyright © 2012 Hassan Azadi Kenary 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 fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟 2 𝑓 ( ( 𝑥 + 𝑦 + 𝑧 ) / 𝑟 ) + 𝑟 2 𝑓 ( ( 𝑥 − 𝑦 + 𝑧 ) / 𝑟 ) + 𝑟 2 𝑓 ( ( 𝑥 + 𝑦 − 𝑧 ) / 𝑟 ) + 𝑟 2 𝑓 ( ( − 𝑥 + 𝑦 + 𝑧 ) / 𝑟 ) = 4 𝑓 ( 𝑥 ) + 4 𝑓 ( 𝑦 ) + 4 𝑓 ( 𝑧 ) , where 𝑟 is a positive real number, in non-Archimedean normed spaces.