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Báo cáo hóa học: " Research Article Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions"

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 Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 210340 14 pages doi 10.1155 2010 210340 Research Article Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions Songnian He 1 2 Yongfu Su 3 and Ronghua Li1 1 College of Science Civil Aviation University of China Tianjin 300300 China 2 Tianjin Key Laboratory for Advanced Signal Processing Civil Aviation University of China Tianjin 300300 China 3 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Songnian He songnianhe2005@yahoo.com.cn Received 25 September 2010 Accepted 19 December 2010 Academic Editor Satit Saejung Copyright 2010 Songnian He 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. Let C be a nonempty closed convex subset of a real Hilbert space H and let T C H be a boundedly Lipschitzian strong pseudo-contraction with a nonempty fixed point set. Three iterative algorithms are proposed for approximating the unique fixed point of T one of them is for the selfmapping case and the others are for the nonself-mapping case. Not only the strong convergence but also the degree of convergence of the three iterative algorithms is obtained. Some numerical results corresponding to the self-mapping case are given which show advantages of our methods. As an application of our results adopting the regularization idea we also propose implicit and explicit algorithms for approximating a fixed point of a boundedly Lipschitzian pseudocontractive self-mapping from C into itself respectively. 1. Introduction and Preliminaries Let H be a real Hilbert space with inner product and norm II II and let C be a nonempty closed convex subset of H. Recall that a mapping T C H is said to be pseudo-contractive if Tx - Ty x - y x