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)
• Published : 2006.08.01
• 144 20

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

References

1. J. Aczel, and J. Dhombres, Functional equations in several variables, Cambridge Univ. Press, Cambridge, 1989
2. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 https://doi.org/10.1006/jmaa.1994.1211
3. S.-H. Lee, Stability of a quadratic Jensen type functional equation, Korean J. Comput. & Appl. Math. (Series A) 9 (2002), no. 1, 389-399
4. Y.-W. Lee, On the stability of a quadratic Jensen type functional equation, J. Math. Anal. Appl. 270 (2002), no. 2, 590-601 https://doi.org/10.1016/S0022-247X(02)00093-8
5. S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1960
6. Y.-W. Lee, Stability of a generalized quadratic functional equation with Jensen type, Bull. Korean Math. Soc. 42 (2005), no. 1, 57-73 https://doi.org/10.4134/BKMS.2005.42.1.057
7. Th. M. Rassias, On the stability of the linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300
8. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224

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