Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 198098, 11 pages
doi:10.1155/2010/198098
Research Article

On the Stability of Generalized Quartic Mappings in Quasi-β-Normed Spaces

Dongseung Kang

Department of Mathematical Education, Dankook University, 126 Jukjeon, Suji, Yongin, Gyeonggi 448-701, South Korea

Received 28 August 2009; Revised 7 December 2009; Accepted 25 January 2010

Academic Editor: Patricia J. Y. Wong

Copyright © 2010 Dongseung Kang. 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 generalized quartic function f:X→Y such that f(ax+by)+f(ax−by)−2a2(a2−b2)f(x)=(ab)2[f(x+y)+f(x−y)]−2b2(a2−b2)f(y), where a≠0, b≠0, a±b≠0, for all x,y∈X.