Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401762, 9 pages
http://dx.doi.org/10.1155/2012/401762
Research Article

Stability of the 𝑛 -Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces

Yang-Hi Lee,1 Soon-Mo Jung,2 and Themistocles M. Rassias3

1Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, Republic of Korea
2Mathematics Section, College of Science and Technology, Hongik University, 339-701 Jochiwon, Republic of Korea
3Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Received 19 November 2011; Accepted 23 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Yang-Hi Lee 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 will prove the stability of the functional equation ∑ 2 𝑓 ( 𝑛 𝑖 = 1 𝑥 𝑖 ∑ ) + 1 ≤ 𝑖 , 𝑗 ≤ 𝑛 , 𝑖 ≠ 𝑗 𝑓 ( 𝑥 𝑖 − 𝑥 𝑗 ) = ∑ ( 𝑛 + 1 ) 𝑛 𝑖 = 1 𝑓 ( 𝑥 𝑖 ∑ ) + ( 𝑛 − 1 ) 𝑛 𝑖 = 1 𝑓 ( − 𝑥 𝑖 ) in non-Archimedean normed spaces.