Journal of Applied Mathematics
Volume 2012 (2012), Article ID 547865, 15 pages
http://dx.doi.org/10.1155/2012/547865
Research Article

Stability of an 𝑛 -Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

Yang-Hi Lee1 and Soon-Mo Jung2

1Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, Republic of Korea
2Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, Republic of Korea

Received 5 August 2011; Accepted 28 November 2011

Academic Editor: Xianhua Tang

Copyright © 2012 Yang-Hi Lee and Soon-Mo Jung. 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 stability problems for the 𝑛 -dimensional mixed-type additive and quadratic functional equation ∑ 2 𝑓 ( 𝑛 𝑗 = 1 𝑥 𝑗 ∑ ) + 1 ≤ 𝑖 , 𝑗 ≤ 𝑛 , 𝑖 ≠ 𝑗 𝑓 ( 𝑥 𝑖 − 𝑥 𝑗 ∑ ) = ( 𝑛 + 1 ) 𝑛 𝑗 = 1 𝑓 ( 𝑥 𝑗 ∑ ) + ( 𝑛 − 1 ) 𝑛 𝑗 = 1 𝑓 ( − 𝑥 𝑗 ) in random normed spaces by applying the fixed point method.