On the Hyers-Ulam-Rassias Stability of the Bi-Jensen Functional Equation

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.705-720
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.705
Title & Authors
On the Hyers-Ulam-Rassias Stability of the Bi-Jensen Functional Equation
Jun, Kil-Woung; Han, Mi-Hyen; Lee, Yang-Hi;

Abstract
In this paper, we obtain the Hyers-Ulam-Rassias stability of a bi-Jensen functional equation $4f(\frac {x+y}{2},\;\frac {z+w}{2}) Keywords Hyers-Ulam-Rassias stability;bi-Jensen mapping;functional equation; Language English Cited by References 1. J. H. Bae and W. G. Park, On the solution of bi-Jensen functional equation and its stability, Bull. Korean Math. Soc., 43(2006), 499-507. 2. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. and Appl.,184(1994), 431-436. 3. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A., 27(1941), 222-224. 4. K. W. Jun, Y. H. Lee and Y. S. Cho, On the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation, Abstract Appl. Anal., ID 35151(2007), 1-15. 5. K. W. Jun, Y. H. Lee and J. H. Oh, On the Rassias stability a bi-Jensen functional equation, preprint. 6. S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, Jour Appl. Math. Lett., 17(2004), 1135-1140. 7. G. H. Kim. On the stability of functional equations with square-symmetric operation, Jour Math. Inequal. Appl., 4(2001), 257-266. 8. H. M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl., 324(2006), 358-372. 9. Y. H. Lee and K. W. Jun, On the stability of approximately additive mappings, Jour Proc. Amer. Math. Soc., 128(2000), 1361-1369. 10. C. G. Park, Linear functional equations in Banach modules over a$C^{\ast}-algebra\$, Acta Appl. Math., 77(2003), 125-161.

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S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1968, p. 63.