Abstract and Applied Analysis
Volume 2012 (2012), Article ID 482936, 14 pages
http://dx.doi.org/10.1155/2012/482936
Research Article

A Fixed Point Approach to the Stability of an 𝑛 -Dimensional Mixed-Type Additive and Quadratic Functional Equation

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 8 October 2011; Accepted 3 December 2011

Academic Editor: Alberto d'Onofrio

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 a 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 ) by using the fixed point method.