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Commun. Korean Math. Soc. 2008; 23(3): 377-386

Printed September 1, 2008

Copyright © The Korean Mathematical Society.

On the stability of a Cauchy-Jensen functional equation

Kil-Woung Jun, Yang-Hi Lee, and Young-Sun Cho

Chungnam National University, Gongju National University of Education, Chungnam National University

Abstract

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In this paper, we prove the stability of a Cauchy-Jensen functional equation $$2f ( x+y , \frac{z + w }2 ) = f (x,z)+ f (x,w)+ f (y,z)+ f (y,w) $$ in the sense of Th. M. Rassias.

Keywords: stability, Cauchy-Jensen mapping, functional equation

MSC numbers: Primary 39B52

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