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SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

이재하|김광휘|이영환
한국수학교육학회|2008.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제15권 제2호|pp. 169-178

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참고문헌

키워드

exponential functional equationstability of functional equationsuper- stabilitysolution of functional equation.
주제분류수학

초록

In this paper we generalize the superstability of the exponential func- tional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation f(x + y) = axyf(x)f(y) and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting : f(x + y) axyf(x)f(y) ¡ 1 · ±:

Abstract

In this paper we generalize the superstability of the exponential func- tional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation f(x + y) = axyf(x)f(y) and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting : f(x + y) axyf(x)f(y) ¡ 1 · ±:

참고문헌 (22)

  1. J. Baker, "The stability of the cosine equations", Proc. Amer. Math. Soc, 80, pp.411~416 (1980)
  2. J. Baker, "The stability of the equation f(x+y) = f(x)+f(y)", Proc. Amer. Math. Soc, 74, pp.242~246 (1979)
  3. G.L. Forti, "Hyers-Ulam stability of functional equations in several variables", Aequa-tiones Math, 50, pp.146~190 (1995)
  4. R. Ger, "Superstability is not natural. Rocznik Naukowo-Dydaktyczny WSP Krakkowie", Prace Mat, 159, pp.109~123 (1993)
  5. D.H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U. S. A, 27, pp.222~224 (1941)
  6. D.H. Hyers, "Approximate homomorphisms", Aequatioues Math, 44, pp.125~153 (1992)
  7. D.H. Hyers, "Stability of functional equations in several variables" (1998), Birkhauser-Basel-Berlin
  8. K.-W. Jun, "Stability of generalized gamma and beta functional equations", Aequationes Math, 60, pp.15~24 (2000)
  9. S.-M. Jung, "On the general Hyers-Ulam stability of gamma functional equation", Bull. Korean Math. Soc, 34(3), pp.437~446 (1997)
  10. S.-M. Jung, "On the stability of the gamma functional equation", Results Math, 33, pp.306~309 (1998)
  11. G.H. Kim, "The stability of the beta functional equation", Babes-Bolyai Mathematica, XLV(1), pp.89~96 (2000)
  12. Y.W. Lee, "On the stability of a quadratic Jensen type functional equation", J. Math. Anal. Appl, 270, pp.590~601 (2002)
  13. Y.W. Lee, "The stability of derivations on Banach algebras", Bull. Institute of Math. Academia Sinica, 28, pp.113~116 (2000)
  14. Y.W. Lee, "The stability of Cauchy's gamma-beta functional equation", J. Math. Anal. Appl, 299, pp.305~313 (2004)
  15. Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  16. Th.M. Rassias, "On a problem of S. M. Ulam and the asymptotic stability of the Cauchy functional equation with applications. General Inequalities 7. MFO. Oberwol-fach", Oberwol-fach. Birkhauser Verlag. Basel ISNM, 123, pp.297~309 (1997)
  17. Th.M. Rassias, "On the stability of the quadratic functional equation and its applications", Studia. Univ. Babes-Bolyai, XLIII(3), pp.89~124 (1998)
  18. Th.M. Rassias, "The problem of S. M. Ulam for approximately multiplication mappings", J. Math. Anal. Appl, 246, pp.352~378 (2000)
  19. Th.M. Rassias, "On the stability of functional equation in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
  20. Th.M. Rassias, "On the stability of functional equations and a problem of Ulam", ActaApplications Math, 62, pp.23~130 (2000)
  21. Th.M. Rassias, "On the behavior of mapping that do not satisfy Hyers-Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
  22. S.M. Ulam, "Problems in Modern Mathematics" (1964), Wiley

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