Ulam’s Type Stability of Involutional-Exponential Functional Equations

Author:

Chung Jaeyoung1ORCID

Affiliation:

1. Department of Mathematics, Kunsan National University, Gunsan 573-701, Republic of Korea

Abstract

LetSbe a commutative semigroup,f,g:SCandσ:SSan involution. In this paper we consider the stability of involution-exponential functional equationsfx+σy-gxfyϕxresp.,  ϕy, |f(x+σy)-f(x)g(y)|ϕ(x) [resp.,  ϕ(y)]for allx,yS, whereϕ:SR+satisfies the growth condition: there existsC>1such thatlimkC-kϕ(kx)=0for eachxS. We also consider the stability ofL-version|f(x+σy)-f(x)f(y)|L(R2n)ϵ,wheref:RnCis a locally integrable function.

Funder

National Research Foundation of Korea

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

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