Superstability of a generalized exponential functional equation of Pexider type
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We obtain the superstability of a generalized exponential functional equation f(x + y) = E(x, y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: [수식] where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy’s gamma-beta functional equation.
Abstract
We obtain the superstability of a generalized exponential functional equation f(x + y) = E(x, y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: [수식] where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy’s gamma-beta functional equation.
참고문헌 (17)
- J. Baker, "The stability of the cosine equations", Proc. Amer. Math. Soc, 80, pp.411~416 (1980)
- J. Baker, "The stability of the equation f(x + y) = f(x) + f(y)", Proc. Amer. Math. Soc, 74, pp.242~246 (1979)
- G. L. Forti, "Hyers-Ulam stability of functional equations in several variables", Aequationes Math, 50, pp.146~190 (1995)
- R. Ger, "Superstability is not natural, Rocznik Naukowo-Dydaktyczny WSP Krakkowie", Prace Mat, 159, pp.109~123 (1993)
- D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U. S. A, 27, pp.222~224 (1941)
- D. H. Hyers, "Approximate homomorphisms", Aequatioues Math, 44, pp.125~153 (1992)
- D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkh¨auser-Basel-Berlin
- K. W. Jun, "Stability of generalized gamma and beta functional equations", Aequation Math, 60, pp.15~24 (2000)
- S.-M. Jung, "On the general Hyers-Ulam stability of gamma functional equation", Bull. Korean Math. Soc, 34(3), pp.437~446 (1997)
- S.-M. Jung, "On the stability of the gamma functional equation", Results Math, 33, pp.306~309 (1998)
- G. H. Kim, "The stability of the beta functional equation", Babes-Bolyai Mathematica, (1), pp.89~96 (2000)
- Y. W. Lee, "On the stability of a quadratic Jensen type functional equation", J. Math. Anal. Appl, 270, pp.590~601 (2002)
- Y. W. Lee, "The stability of derivations on Banach algebras", Bull. Institute of Math. Academia Sinica, 28, pp.113~116 (2000)
- Y. W. Lee, "The stability of Cauchy’s gamma-beta functional equation", J. Math. Anal. Appl, 299, pp.305~313 (2004)
- Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- Th. M. Rassias, "The problem of S. M. Ulam for approximately multiplication mappings", J. Math. Anal. Appl, 246, pp.352~378 (2000)
- S. M. Ulam, "Problems in Modern Mathematics, Proc. Chap. VI" (1964), Wiley