Abstract and Applied Analysis
Volume 2012 (2012), Article ID 285807, 12 pages
http://dx.doi.org/10.1155/2012/285807
Research Article

Nearly Quadratic Mappings over 𝑝 -Adic Fields

M. Eshaghi Gordji,1 H. Khodaei,1 and Gwang Hui Kim2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 30 October 2011; Revised 20 November 2011; Accepted 21 November 2011

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 over 𝑝 -adic fields for the generalized quadratic functional equation ∑ 𝑛 𝑘 = 2 ∑ 𝑘 𝑖 1 = 2 ∑ 𝑖 𝑘 + 1 2 = 𝑖 1 + 1 ⋯ ∑ 𝑛 𝑖 𝑛 − 𝑘 + 1 = 𝑖 𝑛 − 𝑘 + 1 ∑ 𝑓 ( 𝑛 𝑖 = 1 , 𝑖 ≠ 𝑖 1 , … , 𝑖 𝑛 − 𝑘 + 1 𝑥 𝑖 − ∑ 𝑛 − 𝑘 + 1 𝑟 = 1 𝑥 𝑖 𝑟 ∑ ) + 𝑓 ( 𝑛 𝑖 = 1 𝑥 𝑖 ) = 2 𝑛 − 1 ∑ 𝑛 𝑖 = 1 𝑓 ( 𝑥 𝑖 ) , where 𝑛 ∈ ℕ and 𝑛 ≥ 2 .