Báo cáo hoa học: " Research Article On Approximate Cubic Homomorphisms"

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 On Approximate Cubic Homomorphisms | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 618463 11 pages doi 2009 618463 Research Article On Approximate Cubic Homomorphisms M. Eshaghi Gordji and M. Bavand Savadkouhi Department of Mathematics Semnan University P. O. Box 35195-363 Semnan Iran Correspondence should be addressed to M. Eshaghi Gordji Received 22 October 2008 Revised 4 March 2009 Accepted 2 July 2009 Recommended by Rigoberto Medina We investigate the generalized Hyers-Ulam-Rassias stability of the system of functional equations f xy f x f y f 2x y f 2x - y 2f x y 2f x - y 12f x on Banach algebras. Indeed we establish the superstability of this system by suitable control functions. Copyright 2009 M. Eshaghi Gordji and M. Bavand Savadkouhi. 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 A definition of stability in the case of homomorphisms between metric groups was suggested by a problem by Ulam 2 in 1940. Let G1 be a group and let G2 be a metric group with the metric d y . Given e 0 does there exist a Ỗ 0 such that if a mapping h G1 G2 satisfies the inequality d h x y h x h y Ỗ for all x y e G1 then there exists a homomorphism H G1 G2 with d h x H x e for all x e G1 In this case the equation of homomorphism h x y h x hy is called stable. On the other hand we are looking for situations when the homomorphisms are stable that is if a mapping is an approximate homomorphism then there exists an exact homomorphism near it. The concept of stability for a functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the equation. In 1941 Hyers 3 gave a positive answer to the question of Ulam for Banach spaces. Let f E1 E2 be a mapping between Banach spaces such that llf x y - f x - f y ll ỗ for all

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