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 a Generalized Euler-Lagrange Type Additive Mapping and Homomorphisms in C∗ | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 273165 22 pages doi 2009 273165 Research Article Stability of a Generalized Euler-Lagrange Type Additive Mapping and Homomorphisms in c-Algebras Abbas Najati1 and Choonkil Park2 1 Department of Mathematics Faculty of Sciences University ofMohaghegh Ardabili Ardabil 56199-11367 Iran 2 Department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Choonkil Park baak@ Received 17 June 2009 Revised 30 July 2009 Accepted 4 August 2009 Recommended by Patricia J. Y. Wong Let X Y be Banach modules over a c -algebra and let r1 . rn e R be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a 1 mi 4-a 1 c al ơ Trr a X1 n _ ft_T V I V r-Y-l I X n y. i y. n t i X1 n T y - A AATia qE i WA7 TE al- a unital c -algebra 2-1 j 1 f rjXj 2-11 i n i j iXi 2 2ji 1 rif Xi nf i 1 rịXị . We show that if ỵn 1 r 0 Ti rj 0 for some 1 i j n and a mapping f X Y satisfies the functional equation mentioned above then the mapping f X Y is Cauchy additive. As an application we investigate homomorphisms in unital c -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 and Preliminaries The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. Theorem Th. M. Rassias 4 . Let f E E be a mapping from a normed vector .
