Abstract and Applied Analysis
Volume 2012 (2012), Article ID 896032, 10 pages
http://dx.doi.org/10.1155/2012/896032
Research Article

Nearly Radical Quadratic Functional Equations in p-2-Normed Spaces

M. Eshaghi Gordji,1 H. Khodaei,2 A. Ebadian,3 and G. H. Kim4

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran
3Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
4Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 16 November 2011; Accepted 13 February 2012

Academic Editor: John Rassias

Copyright © 2012 M. Eshaghi Gordji 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 establish some stability results in 2-normed spaces for the radical quadratic functional equation 𝑓 ( ∑ 𝑛 𝑖 = 1 ( 𝑥 𝑖 + 𝑦 𝑖 ) 2 ) + 𝑓 ( ∑ 𝑛 𝑖 = 1 ( 𝑥 𝑖 − 𝑦 𝑖 ) 2 ) = 2 ∑ 𝑛 𝑖 = 1 ( 𝑓 ( 𝑥 𝑖 ) + 𝑓 ( 𝑦 𝑖 ) ) and then use subadditive functions to prove its stability in 𝑝 -2-normed spaces.