The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS

  • Received : 2009.03.25
  • Accepted : 2010.05.07
  • Published : 2010.05.31
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Abstract

Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

Keywords

References

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