Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 527574, 18 pages
http://dx.doi.org/10.1155/2011/527574
Research Article

On Solution and Stability of a Two-Variable Functional Equations

Y. J. Cho,1 R. Saadati,2 S. Shabanian,3 and S. M. Vaezpour3

1Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran
3Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Received 5 June 2011; Accepted 30 August 2011

Academic Editor: Yihong Song

Copyright © 2011 Y. J. Cho 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

The main purpose of this paper is to investigate the stability of the functional equation 𝑓 ( 𝑥 + 𝑦 , 𝑦 + 𝑧 ) = 2 𝑓 ( 𝑥 / 2 , 𝑦 / 2 ) + 2 𝑓 ( 𝑦 / 2 , 𝑧 / 2 ) in normed spaces. The solutions of such functional equations are considered.