Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 929824, 14 pages
http://dx.doi.org/10.1155/2011/929824
Research Article

Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces

A. Ebadian,1 N. Ghobadipour,1 Th. M. Rassias,2 and M. Eshaghi Gordji3,4,5

1Department of Mathematics, Urmia University, Urmia, Iran
2Department of Mathematics, National Technical University of Athens, 15780 Zografou, Greece
3Department of Mathematics, Semnan University, P.O. Box 35195-363, Iran
4Research Group of Nonlinear Analysis and Applications (RGNAA), Semnan University, Iran
5Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Iran

Received 30 October 2010; Accepted 19 January 2011

Academic Editor: Rigoberto Medina

Copyright © 2011 A. Ebadian 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

We investigate the generalized Hyers-Ulam stability of the functional inequalities ‖ 𝑓 ( ( 𝑥 + 𝑦 + 𝑧 ) / 4 ) + 𝑓 ( ( 3 𝑥 − 𝑦 − 4 𝑧 ) / 4 ) + 𝑓 ( ( 4 𝑥 + 3 𝑧 ) / 4 ) ‖ ≤ ‖ 2 𝑓 ( 𝑥 ) ‖ and ‖ 𝑓 ( ( 𝑦 − 𝑥 ) / 3 ) + 𝑓 ( ( 𝑥 − 3 𝑧 ) / 3 ) + 𝑓 ( ( 3 𝑥 + 3 𝑧 − 𝑦 ) / 3 ) ‖ ≤ ‖ 𝑓 ( 𝑥 ) ‖ in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.