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Báo cáo hoa học: " Research Article A Functional Inequality in Restricted Domains of Banach Modules"

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 A Functional Inequality in Restricted Domains of Banach Modules | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 973709 14 pages doi 10.1155 2009 973709 Research Article A Functional Inequality in Restricted Domains of Banach Modules M. B. Moghimi 1 Abbas Najati 1 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@hanyang.ac.kr Received 28 April 2009 Revised 2 August 2009 Accepted 16 August 2009 Recommended by Binggen Zhang We investigate the stability problem for the following functional inequality af x y 2a Pf .ty z 2p Yf z x 2ỵ ỊỊ f x y z on restricted domains of Banach modules over a c -algebra. As an application we study the asymptotic behavior of a generalized additive mapping. Copyright 2009 M. B. Moghimi 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 following question concerning the stability of group homomorphisms was posed by Ulam 1 Under what conditions does there exist a group homomorphism near an approximate group homomorphism Hyers 2 considered the case of approximately additive mappings f E E where E and E are Banach spaces and f satisfies Hyers inequality Wf x y - f x - f y II 1.1 for all x y e E. In 1950 Aoki 3 provided a generalization of the Hyers theorem for additive mappings and in 1978 Rassias 4 generalized the Hyers theorem for linear mappings by allowing the Cauchy difference to be unbounded see also 5 . The result of Rassias theorem has been generalized by Forti 6 7 and Gavruta 8 who permitted the Cauchy difference to be bounded by a general control function. During the last three decades a number of papers 2 Advances in Difference Equations have been published