Korean J. Math.  Vol 20, No 2 (2012)  pp.
DOI: https://doi.org/10.11568/kjm.2012.20.2.

SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP

Gwang Hui Kim

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 → R are unknown mappings and m is a fixed positive integer. Here G is an Abelian group (G,+), and R the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. Gavruta’s result in 1994 and G. H. Kim’s results in 2011. 


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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr