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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.17 No.2

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APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.2, pp.115-130
Park, Kyoo-Hong
Jung, Yong-Soo
Park,, K. , & Jung,, Y. (2010). APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(2), 115-130.

Abstract

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

keywords
quadratic derivation, approximate quadratic derivation, stability

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