Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 79816, 3 pages
doi:10.1155/2007/79816
Research Article
On Stability of a Functional Equation Connected with the Reynolds Operator
Institute of Mathematics, University of Rzeszów, Rejtana 16A, Rzeszów 35-310, Poland
Received 18 July 2006; Revised 30 November 2006; Accepted 3 December 2006
Academic Editor: Saburou Saitoh
Copyright © 2007 Adam Najdecki. 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
Let (X,∘) be an Abelain semigroup, g:X→X, and let K
be either ℝ or ℂ. We prove superstability of the functional equation f(x∘g(y))=f(x)f(y) in the class of functions f:X→K. We also show some stability results of the equation in the class of functions f:X→Kn.