대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제48권5호
  • /
  • Pages.959-967
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  • 2011
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS

  • 투고 : 2010.02.01
  • 발행 : 2011.09.30
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초록

Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

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