tailieunhanh - Báo cáo hóa học: " Research Article Fixed Points and Stability of the Cauchy "

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 Fixed Points and Stability of the Cauchy | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 809232 14 pages doi 2009 809232 Research Article Fixed Points and Stability of the Cauchy Functional Equation in C -Algebras Choonkil Park Department of Mathematics Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Choonkil Park baak@ Received 8 December 2008 Accepted 9 February 2009 Recommended by Tomas Dominguez Benavides Using the fixed point method we prove the generalized Hyers-Ulam stability of homomorphisms in C -algebras and Lie C -algebras and of derivations on C -algebras and Lie C -algebras for the Cauchy functional equation. Copyright 2009 Choonkil 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. 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 obtained by Gavruta 5 by replacing the unbounded Cauchy difference by a general control function in the spirit of Th. M. Rassias approach. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem see 6-19 . J. M. Rassias 20 21 following the spirit of the innovative approach of Th. M. Rassias 4 for the unbounded Cauchy difference .