Journal of Applied Mathematics
Volume 2011 (2011), Article ID 540274, 10 pages
http://dx.doi.org/10.1155/2011/540274
Research Article

Stability of the Pexiderized Lobacevski Equation

Gwang Hui Kim

Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 16 April 2011; Accepted 11 June 2011

Academic Editor: Junjie Wei

Copyright © 2011 Gwang Hui Kim. 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

The aim of this paper is to investigate the solution and the superstability of the Pexiderized Lobacevski equation 𝑓 ( ( 𝑥 + 𝑦 ) / 2 ) 2 = 𝑔 ( 𝑥 ) ℎ ( 𝑦 ) , where 𝑓 , 𝑔 , ℎ  :  𝐺 2 → ℂ are unknown functions on an Abelian semigroup ( 𝐺 , + ) . The obtained result is a generalization of Gǎvruţa's result in 1994 and Kim's result in 2010.