Browse > Article
http://dx.doi.org/10.4134/BKMS.2006.43.3.499

ON THE SOLUTIONS OF A BI-JENSEN FUNCTIONAL EQUATION AND ITS STABILITY  

Bae, Jae-Hyeong (Department of Mathematics and Applied Mathematics, Kyung Hee University)
Park, Won-Gil (National Institute for Mathematical Sciences)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.3, 2006 , pp. 499-507 More about this Journal
Abstract
In this paper, we obtain the general solution and the stability of the hi-Jensen functional equation $$4f(\frac {x+y} 2,\;\frac {z+w} 2)=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$.
Keywords
solution; stability; bi-Jensen mapping; functional equation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 10
연도 인용수 순위
1 Y.-W. Lee, Stability of a generalized quadratic functional equation with Jensen type, Bull. Korean Math. Soc. 42 (2005), no. 1, 57-73   과학기술학회마을   DOI   ScienceOn
2 J. Aczel, and J. Dhombres, Functional equations in several variables, Cambridge Univ. Press, Cambridge, 1989
3 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436   DOI   ScienceOn
4 S.-H. Lee, Stability of a quadratic Jensen type functional equation, Korean J. Comput. & Appl. Math. (Series A) 9 (2002), no. 1, 389-399
5 Y.-W. Lee, On the stability of a quadratic Jensen type functional equation, J. Math. Anal. Appl. 270 (2002), no. 2, 590-601   DOI   ScienceOn
6 S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1960
7 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224
8 Th. M. Rassias, On the stability of the linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300