Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 79816, 3 pages
Research Article

On Stability of a Functional Equation Connected with the Reynolds Operator

Adam Najdecki

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.


Let (X,) be an Abelain semigroup, g:XX, and let K be either or . We prove superstability of the functional equation f(xg(y))=f(x)f(y) in the class of functions f:XK. We also show some stability results of the equation in the class of functions f:XKn.