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Superstability of multiplicative linear mappings

Ehsan Anjidani|Esmaeil Ansari-Piri
대한수학회 (The Korean Mathematical Society)|2011.04|대한수학회논문집 (Communications of the KMS)|제26권 제2호|pp. 253-259

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참고문헌

키워드

stability of functional equationsuperstabilityalgebra homomorphism
주제분류수학

초록

Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f:A → B, in the sense of Rassias, is an algebra homomorphism.

Abstract

Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f:A → B, in the sense of Rassias, is an algebra homomorphism.

참고문헌 (13)

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  2. D. G. Bourgin, "Approximately isometric and multiplicative transformations on contin- uous function rings", Duke Math. J, 16, pp.385~397 (1949)
  3. J. Brzdek, "A note on stability of the general linear equation", Aequationes Math, 75(3), pp.267~270 (2008)
  4. S. Czerwik, "Stability of Functional Equations of Hyers-Ulam-Rassias Type" (2003), Hadronic Press Inc
  5. M. Eshaghi Gordji, "Stability of an additive-quadratic functional equation of two variables in F-spaces", J. Nonlinear Sci. Appl, 2(4), pp.251~259 (2009)
  6. G. L. Forti, "Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations", J. Math. Anal. Appl, 295(1), pp.127~133 (2004)
  7. J. Math. Anal. Appl, "A generalization of the Hyers-Ulam-Rassias stability of approximately ad- ditive mappings", 431{436, 184(3), pp.431~436 (1994)
  8. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
  9. D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser
  10. A. Najati, "Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in Cꠗ-algebras", J. Nonlinear Sci. Appl, 3(2), pp.123~143 (2010)
  11. C. Park, "On an approximate automorphism on a C-algebra", Proc. Amer. Math. Soc, 132(6), pp.1739~1745 (2004)
  12. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72(2), pp.297~300 (1978)
  13. S. M. Ulam, "Problems in Modern Mathematics" (1964), Science Editions, Wiley

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