tailieunhanh - Báo cáo hóa học: "Research Article Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces"

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 Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 279058 7 pages doi 2009 279058 Research Article Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces Yonghong Yao 1 Yeong Cheng Liou 2 and Giuseppe Marino3 1 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China 2 Department of Information Management Cheng Shiu University Kaohsiung 833 Taiwan 3 Dipartimento di Matematica Universita della Calabria 87036 Arcavacata di Rende CS Italy Correspondence should be addressed to Yonghong Yao yaoyonghong@ Received 6 April 2009 Accepted 12 September 2009 Recommended by Simeon Reich We introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed algorithms strongly converge to a fixed point of a nonexpansive mapping T. Copyright 2009 Yonghong Yao 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 Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping T C C is said to be nonexpansive if Tx - Ty x - y M for all x y e C. We use Fix T to denote the set of fixed points of T. Construction of fixed points of nonlinear mappings is an important and active research area. In particular iterative algorithms for finding fixed points of nonexpansive mappings have received vast investigation cf. 1 2 since these algorithms find applications in a variety of applied areas of inverse problem partial differential equations image recovery and signal processing see 3-8 . Iterative methods for nonexpansive mappings have been extensively investigated in the literature see 1-7 9-21 . It is our purpose in this paper to introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed .