ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION

Koh, Hee-Jeong; Kang, Dong-Seung

doi:10.4134/BKMS.2008.45.4.739

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ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION

Journal title : Bulletin of the Korean Mathematical Society
Volume 45, Issue 4, 2008, pp.739-748
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2008.45.4.739

Title & Authors

ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION
Koh, Hee-Jeong; Kang, Dong-Seung;

Abstract

In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation ${$$4f(\sum_{j=1}^{n-1}\;x_j\;+\;mx_n)\;+\;4f(\sum_{j=1}^{n-1}\;x_j+mx_n\;x_j\;-\;mx_n}\;+\;m^2\sum_{j=1}^{n-1}\;(f(2x_j)\;=\;8f(\sum_{j=1}^{n-1}\;x_j)\;+\;4m^2{\sum_{j=1}^{n-1}}\;$f(x_j+x_n)\;+\;f(x_j-x_n)$$$}$ for a positive integer ${$m\;{\geq}\;1$}$ .

Keywords

Hyers-Ulam-Rassias stability;cubic mapping;

Language

English

Cited by

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Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, Journal of Intelligent & Fuzzy Systems, 2016, 30, 4, 2309

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