On Stability of a Functional Equation Connected with the Reynolds Operator

Let (X,∘) be an Abelain semigroup, g:X→X, and let K be either ℠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....

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Bibliographic Details
Main Author: Adam Najdecki
Format: Article
Language:English
Published: SpringerOpen 2007-01-01
Series:Journal of Inequalities and Applications
Online Access:http://dx.doi.org/10.1155/2007/79816
Description
Summary:Let (X,∘) be an Abelain semigroup, g:X→X, and let K be either ℠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.
ISSN:1025-5834
1029-242X