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ISSN : 1226-0657

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Vol.15 No.2

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A FUNCTIONAL EQUATION ON HOMOGENEOUS POLYNOMIALS

A FUNCTIONAL EQUATION ON HOMOGENEOUSPOLYNOMIALS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.2, pp.103-110
Bae, Jae-Hyeong (COLLEGE OF LIBERAL ARTS, KYUNG HEE UNIVERSITY)
Park, Won-Gil (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES)
Bae, Jae-Hyeong, & Park, Won-Gil. (2008). A FUNCTIONAL EQUATION ON HOMOGENEOUS POLYNOMIALS. 한국수학교육학회지시리즈B:순수및응용수학, 15(2), 103-110.

Abstract

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form <TEX>$f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$</TEX> is a solution of the above functional equation.

keywords
solution, stability, cubic functional equation

한국수학교육학회지시리즈B:순수및응용수학

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