Kyungpook Mathematical Journal

  • 제50권4호
  • /
  • Pages.557-564
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  • 2010
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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A Fixed Point Approach to the Stability of a Functional Equation

  • Park, Won-Gil (Department of Mathematics Education, College of Education, Mokwon University) ;
  • Bae, Jae-Hyeong (College of Liberal Arts, Kyung Hee University)
  • 투고 : 2010.03.19
  • 심사 : 2010.09.03
  • 발행 : 2010.12.31
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초록

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.

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참고문헌

  1. J. H. Bae and W. G. Park, On stability of a functional equation with n variables, Nonlinear Anal. TMA, 64(2006), 856-868. https://doi.org/10.1016/j.na.2005.06.028
  2. J. H. Bae and W. G. Park, On a cubic equation and a Jensen-quadratic equation, Abstarct Appl. Anal., 2007(2007), Article ID 45179.
  3. J. H. Bae and W. G. Park, A fixed point approach to the stability of a functional equation on quadratic forms, preprint.
  4. L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4(2003), Article 4.
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  9. W. G. Park and J. H. Bae, A multidimensional functional equation having quadratic forms as solutions, J. Inequal. Appl., 2007(2007), Article ID 24716.
  10. W. G. Park and J. H. Bae, A functional equation related to quadratic forms without the cross product terms, Honam Math. J., 30(2008), 219-225. https://doi.org/10.5831/HMJ.2008.30.2.219
  11. W. G. Park and J. H. Bae, A functional equation originating from elliptic curves, Abstract Appl. Anal., 2008(2008), Article ID 135237.
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