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APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS  

Park, Kyoo-Hong (DEPARTMENT OF MATHEMATICS EDUCATION, SEOWON UNIVERSITY)
Jung, Yong-Soo (DEPARTMENT OF MATHEMATICS, SUN MOON UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.17, no.2, 2010 , pp. 115-130 More about this Journal
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
quadratic derivation; approximate quadratic derivation; stability;
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