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ON THE STABILITY OF MODULE LEFT DERIVATIONS IN BANACH ALGEBRAS

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In this paper, we improve the generalized Hyers-Ulam stability and the superstability of module left derivations due to the results of [7].

Abstract

In this paper, we improve the generalized Hyers-Ulam stability and the superstability of module left derivations due to the results of [7].

참고문헌 (12)

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  2. Z. Gajda, "On stability of additive mappings", Internat. J. Math. Math. Sci, 14, pp.431~434 (1991)
  3. P. G·avruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  4. P. G·avruta, "An answer to a question of J.M. Rassias concerning the stability of Cauchy equation. in: Advances in Equations and Inequalities, in: Hadronic Math. Ser", ~71 (1999)
  5. D.H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci, 27, pp.222~224 (1941)
  6. S.-M. Jung, "Hyers-Ulam-Rassias Stability of Functional equations in Mathematical Analysis" (2001), Hadronic Press, Inc
  7. Y.-S. Jung, "On the generalized Hyers-Ulam stability of module left derivations", J. Math. Anal. Appl, 339, pp.108~114 (2008)
  8. T. Miura, "A perturbation of ring derivations on Banach algebras", J. Math. Anal. Appl, 319, pp.522~530 (2006)
  9. J.M. Rassias, "On Approximation of Approximately Linear Mappings by Linear Map- pings", J. Funct. Anal. USA, 46, pp.126~130 (1982)
  10. Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  11. P. Semrl, "The functional equation of multiplicative derivation is superstable on stan- dard operator algebras", Integr. Equat. Oper. Theory, 18, pp.118~122 (1994)
  12. S.M. Ulam, "Collection of Mathematical Problems" (1960), Interscience Publ

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