tailieunhanh - Báo cáo hóa học: " Research Article Stability of Homomorphisms and Generalized Derivations on Banach Algebras"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Stability of Homomorphisms and Generalized Derivations on Banach Algebras | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 595439 12 pages doi 2009 595439 Research Article Stability of Homomorphisms and Generalized Derivations on Banach Algebras Abbas Najati1 and Choonkil Park2 1 Department of Mathematics Faculty of Sciences University ofMohaghegh Ardabili Ardabil 56199-11367 Iran 2 Department of Mathematics Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Choonkil Park baak@ Received 14 June 2009 Accepted 18 November 2009 Recommended by Sin-Ei Takahasi We prove the generalized Hyers-Ulam stability of homomorphisms and generalized derivations associated to the following functional equation f 2x y f x 2y f 3x f 3y on Banach algebras. Copyright 2009 A. Najati and C. Park. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The first stability problem concerning group homomorphisms was raised from a question of Ulam 1 Let G1z be a group and let G2 d be a metric group with the metric dfi . Given 0 does there exist 5 e 0 such that if a mapping h G1 G2 satisfies the inequality d h x y h x hfiy Ỗ for all x y e G1 then there is a homomorphism H G1 G2 with d h x H x e 1-1 1-2 for all x e G1 Hyers 2 gave a first affirmative answer to the question of Ulam for Banach spaces Aoki 3 and Rassias 4 provided a generalization of the Hyers theorem for additive and linear mappings respectively by allowing the Cauchy difference to be unbounded see also 5 - 2 Journal of Inequalities and Applications Theorem Rassias . Let f E E be a mapping from a normed vector space E into a Banach space E subject to the inequality f x y - f x - f y ll llxllp l y p for all x y e E where and p are constants with 0 and p 1. Then the limit L x lim n tt 2n exists for all x e E and L E E is the .