tailieunhanh - Báo cáo hóa học: "Research Article Strong Convergence Theorems for Infinitely Nonexpansive Mappings in Hilbert Space Yi-An Chen"

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 Theorems for Infinitely Nonexpansive Mappings in Hilbert Space Yi-An Chen | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 962303 7 pages doi 2009 962303 Research Article Strong Convergence Theorems for Infinitely Nonexpansive Mappings in Hilbert Space Yi-An Chen College of Mathematics and Statistics Chongqing Technology and Business University Chongqing 400067 China Correspondence should be addressed to Yi-An Chen chenyian1969@ Received 23 June 2009 Accepted 12 October 2009 Recommended by Anthony To Ming Lau We introduce a modified Ishikawa iterative process for approximating a fixed point of two infinitely nonexpansive self-mappings by using the hybrid method in a Hilbert space and prove that the modified Ishikawa iterative sequence converges strongly to a common fixed point of two infinitely nonexpansive self-mappings. Copyright 2009 Yi-An Chen. 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 Hilbert space H T a self-mapping of C. Recall that T is said to be nonexpansive if Tx - Ty x - yịị for all x y e C. Construction of fixed points of nonexpansive mappings via Mann s iteration 1 has extensively been investigated in literature see . 2-5 and reference therein . But the convergence about Mann s iteration and Ishikawa s iteration is in general not strong see the counterexample in 6 . In order to get strong convergence one must modify them. In 2003 Nakajo and Takahashi 7 proposed such a modification for a nonexpansive mapping T. Consider the algorithm x0 e C chosen arbitrarity yn anxn 1 - an Txn Cn v e C yn - v x - v Qn v e C x - v xn - xq 0 xn 1 PCnHQn xq 2 Fixed Point Theory and Applications where Pc denotes the metric projection from H onto a closed convex subset C of H. They prove the sequence xn generated by that algorithm converges strongly to