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

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

Recommended by Saburou Saitoh

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.