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 Additive Functional Inequalities in Banach Modules | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 592504 10 pages doi 2008 592504 Research Article Additive Functional Inequalities in Banach Modules Choonkil Park 1 Jong Su An 2 and Fridoun Moradlou3 1 Department of Mathematics Hanyang University Seoul 133-791 South Korea 2 Department of Mathematics Education Pusan National University Pusan 609-735 South Korea 3 Faculty of Mathematical Science University of Tabriz Tabriz 5166 15731 Iran Correspondence should be addressed to Jong Su An jsan63@ Received 1 April 2008 Revised 4 June 2008 Accepted 10 November 2008 Recommended by Alberto Cabada We investigate the following functional inequality 2f x 2f y 2f z - f x y - f y z f x z in Banach modules over a c -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a c -algebra in the spirit of the Th. M. Rassias stability approach. Moreover these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras. Copyright 2008 Choonkil Park et al. 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. The 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. The paper of Th. M. Rassias 4 has provided a lot of influence in the development of what we call generalized Hyers-Ulam stability of functional equations. A generalization of the Th. M. Rassias theorem was .
