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Báo cáo hóa học: "Research Article A Fixed Point Approach to the Stability of a Quadratic Functional Equation in C∗ -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 A Fixed Point Approach to the Stability of a Quadratic Functional Equation in C∗ -Algebras | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 256165 10 pages doi 10.1155 2009 256165 Research Article A Fixed Point Approach to the Stability of a Quadratic Functional Equation in C -Algebras Mohammad B. Moghimi 1 Abbas Najati 1 and Choonkil Park2 1 Department of Mathematics Faculty of Sciences University ofMohaghegh Ardabili 56199-11367 Ardabil Iran 2 Department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Abbas Najati a.nejati@yahoo.com Received 18 May 2009 Accepted 31 July 2009 Recommended by Tocka Diagana We use a fixed point method to investigate the stability problem of the quadratic functional equation f x y f x - y 2f Ựxx yy in C -algebras. Copyright 2009 Mohammad 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 In 1940 the following question concerning the stability of group homomorphisms was proposed by Ulam 1 Under what conditions does there exist a group homomorphism near an approximately group homomorphism In 1941 Hyers 2 considered the case of approximately additive functions f E E where E and E are Banach spaces and f satisfies Hyers inequality f x y - f x - f y ll e Ơ.1 for all x y E. Aoki 3 and Th. M. Rassias 4 provided a generalization of the Hyers theorem for additive mappings and for linear mappings respectively by allowing the Cauchy difference to be unbounded see also 5 . Theorem 1.1 Th. M. 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 - fy II Hllxllp IlylD 1.2 2 Advances in Difference Equations for all x y e E where e and p are constants with e 0 and p 1. Then the limit T -f x L x Jim L3 n O 2n exists for all x e E and L E E