Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 985348, 16 pages
doi:10.1155/2010/985348
Research Article

Superstability of Some Pexider-Type Functional Equation

Gwang Hui Kim

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

Received 27 August 2010; Revised 18 October 2010; Accepted 19 October 2010

Academic Editor: Andrei Volodin

Copyright © 2010 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

We will investigate the superstability of the sine functional equation from the following Pexider-type functional equation 𝑓 ( 𝑥 + 𝑦 ) + 𝑔 ( 𝑥 − 𝑦 ) = 𝜆 ⋅ ℎ ( 𝑥 ) 𝑘 ( 𝑦 ) ( 𝜆 ∶ c o n s t a n t ), which can be considered the mixed functional equation of the sine and cosine functions, the mixed functional equation of the hyperbolic sine and hyperbolic cosine functions, and the exponential-type functional equations.