Browse > Article
http://dx.doi.org/10.4134/CKMS.2008.23.3.377

ON THE STABILITY OF A CAUCHY-JENSEN FUNCTIONAL EQUATION  

Jun, Kil-Woung (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Lee, Yang-Hi (DEPARTMENT OF MATHEMATICS EDUCATION GONGJU NATIONAL UNIVERSITY OF EDUCATION)
Cho, Young-Sun (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.3, 2008 , pp. 377-386 More about this Journal
Abstract
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;
Citations & Related Records

Times Cited By SCOPUS : 1
연도 인용수 순위
1 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. and Appl. 184 (1994), 431-436   DOI   ScienceOn
2 Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation, J. Chungcheong Math. Soc. 20 (2007), 163-172
3 W.-G. Park and J.-H. Bae, On a Cauchy-Jensen functional equation and its stability, J. Math. Anal. Appl. 323 (2006), 634-643   DOI   ScienceOn
4 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300   DOI
5 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224   DOI   ScienceOn
6 S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1968