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J. Korean Math. Soc. 2004; 41(3): 501-511

Printed May 1, 2004

Copyright © The Korean Mathematical Society.

A generalization of the Hyers-Ulam-Rassias stability of a functional equation of Davison

Kil-Woung Jun, Soon-Mo Jung, and Yang-Hi Lee

Chungnam National University, Hong-Ik University, Kongju National University of Education

Abstract

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We prove the Hyers-Ulam-Rassias stability of the Dav-ison functional equation $f(xy)+f(x+y)=f(xy+x)+f(y)$ for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

Keywords: Hyers-Ulam-Rassias stability, Cauchy equation, Pexider equation, Davison equation

MSC numbers: Primary 39B72, 39B52

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