[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2012.20.2.213

SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP

Kim, Gwang Hui (Department of Mathematics Kangnam University)

Publication Information

Korean Journal of Mathematics / v.20, no.2, 2012 , pp. 213-223 More about this Journal

Abstract

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation ${f(x+y)}^m=g(x)h(y)$ , where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G $\check{a}$ vruta's result in 1994 and G. H. Kim's results in 2011.

Keywords

Hyers-Ulam stability; superstability; exponential functional equation; $C^*$ -algebra; generalized Pexider exponential equation;

Citations & Related Records

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