논문KCI 등재
A FUNCTIONAL EQUATION ON HOMOGENEOUSPOLYNOMIALS
한국수학교육학회|2008.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제15권 제2호|pp. 103-110
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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 f(x; y) = ax3 + bx2y + cxy2 + dy3 is a solution of the above functional equation.
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 f(x; y) = ax3 + bx2y + cxy2 + dy3 is a solution of the above functional equation.
참고문헌 (3)
- J. Aczel, "Functional Equations in Several Variables" (1989), Cambridge Univ. Press
- K.-W. Jun, "The generalized Hyers-Ulam-Rassias stability of a cubic func-tional equation", J. Math. Anal. Appl, 274, pp.867~878 (2002)
- W.-G. Park, "On an additive-quadratic functional equation and its stability", J. Appl. Math. & Computing, 18, pp.563~572 (2005)
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