THE APPROXIMATION FOR FUNCTIONAL EQUATION ORIGINATING FROM A CUBIC FUNCTIO

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 2,  2008, pp.233-246
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.2.233
Title & Authors
THE APPROXIMATION FOR FUNCTIONAL EQUATION ORIGINATING FROM A CUBIC FUNCTIO
Lee, Eun-Hwi; Chang, Ick-Soon; Jung, Yong-Soo;

Abstract
In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j Keywords Stability;Cubic function;Fixed point alternative;Quasi-Banach space; Language English Cited by References 1. J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge Univ. Press, (1989). 2. Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, vol. 1, Colloq. Publ. vol. 48, Amer. Math. Soc., Providence, RI, (2000). 3. L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure and Appl. Math. 4 (1) (2003), Art. 4. 4. L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43-52. 5. I.-S. Chang and Y.-S. Jung, Stability for the functional equation of cubic type, J. Math. Anal. Appl. 334 (1) (2007), 85-96. 6. I.-S. Chang, K.-W. Jun and Y.-S. Jung, The modified Hyers-Ulam-Rassias stability of a cubic type functional equation, Math. Ineq. Appl. 8 (4) (2005), 675-683. 7. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436. 8. D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224. 9. D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, (1998). 10. D.H. Hyers, G. Isac and Th.M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific Publ., Co., Singapore, New Jersey, London, (1997). 11. G. Isac and Th.M. Rassias, Stability of$\phi\$-additive mapping: Applications to nonlinear analysis, Internat. J. Math. ans Math. Sci., 19 (1996), 219-228.

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