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On the Superstability of the generalized Sine Functional Equations

김광휘|한미현
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2011.06|한국수학논문집 (Korean Journal of Mathematics)|제19권 제2호|pp. 171-180

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키워드

Hyers-Ulam-Rassias stabilityexponentialsine functional equationsuperstability.
주제분류수학

초록

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations g(x+y)f(x-y)=f(x)^2-f(y)^2f(x+y)g(x-y)=f(x)^2-f(y)^2g(x+y)g(x-y)=f(x)^2-f(y)^2,which does not use his iteration method.

Abstract

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations g(x+y)f(x-y)=f(x)^2-f(y)^2f(x+y)g(x-y)=f(x)^2-f(y)^2g(x+y)g(x-y)=f(x)^2-f(y)^2,which does not use his iteration method.

참고문헌 (12)

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  2. R. Badora, "On some trigonometric functional inequalities, Functional Equations- Results and Advances", pp.3~15 (2002)
  3. J.A. Baker, "The stability of the cosine equation", Proc. Amer. Math. Soc, 80, pp.411~416 (1980)
  4. J.A. Baker, "The stability of the equation f(x+y) = f(x)f(y)", Proc. Amer. Math. Soc, 74, pp.242~246 (1979)
  5. P.W. Cholewa, "The stability of the sine equation", Proc. Amer. Math. Soc, 88, pp.631~634 (1983)
  6. G.L. Forti, "On an alternative functional equation related to the Cauchy equation", Aequationes Math, 24, pp.195~206 (1982)
  7. P. Gavruta, "On the stability of some functional equations, in Stability of Mappings of Hyers-Ulam Type", pp.93~98 (1994)
  8. D.H. Hyers, "On the stability of the linear functional equatinon", Proc. Natl. Acad. Sci. USA, 27, pp.93~101 (1941)
  9. G.H. Kim, "The stability of d'Alembert and Jensen type functional equations", J. Math. Anal. Appl, 325, pp.237~248 (2007)
  10. G.H. Kim, "A stability of the generalized sine functional equations", J. Math. Anal. Appl, 331, pp.886~894 (2007)
  11. G.H. Kim, "On the Stability of the generalized sine functional equations", Acta Math. Sin, 25, pp.965~972 (2009)
  12. S.M. Ulam, "Problems in Modern Mathematics, in Chap.VI, Science editions" (1964), Wiley

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