Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 368981, 9 pages
doi:10.1155/2010/368981
Research Article

Stability Problems of Quintic Mappings in Quasi-β-Normed Spaces

In Goo Cho,1 Dongseung Kang,2 and Heejeong Koh2

1Faculty of Liberal Education, University of Incheon, 12-1 Songdong, YeonsuIncheon 406-772, Republic of Korea
2Department of Mathematical Education, Dankook University, 126 Jukjeon, Suji, Yongin, Gyeonggi 448-701, Republic of Korea

Received 12 March 2010; Accepted 23 April 2010

Academic Editor: Patricia J. Y. Wong

Copyright © 2010 In Goo Cho 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 investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function for the quintic function f:X→Y such that 2f(2x+y)+2f(2x−y)+f(x+2y)+f(x−2y)=20[f(x+y)+f(x−y)]+90f(x), for all x,y∈X.