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 Some Krasnonsel’ski˘-Mann Algorithms and ı the Multiple-Set Split Feasibility Problem | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 513956 12 pages doi 2010 513956 Research Article Some Krasnonsel skii-Mann Algorithms and the Multiple-Set Split Feasibility Problem Huimin He 1 Sanyang Liu 1 and Muhammad Aslam Noor2 3 1 Department of Mathematics Xidian University Xi an 710071 China 2 Mathematics Department COMSATS Institute of Information Technology Islamabad Pakistan 3 Mathematics Department College of Science King Saud University Riyadh 11451 Saudi Arabia Correspondence should be addressed to Huimin He huiminhe@ Received 3 April 2010 Revised 7 July 2010 Accepted 13 July 2010 Academic Editor S. Reich Copyright 2010 Huimin 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. Some variable Krasnonsel skil-Mann iteration algorithms generate some sequences xn yn and zn respectively via the formula Xn 1 1 - Xn Xn OnTN T2T1Xn yn 1 1 - Pn yn Pn SN1 fTiyn Zn 1 1 - tn 1 zn ln 1T n 1 Zn where T Tn mod N and the mod function takes values in 1 2 . N an pn and ỵn are sequences in 0 1 and T1z T2 . TN are sequences of nonexpansive mappings. We will show in a fairly general Banach space that the sequence xn yn zn generated by the above formulas converge weakly to the common fixed point of T1 T2 . TN respectively. These results are used to solve the multiple-set split feasibility problem recently introduced by Censor et al. 2005 . The purpose of this paper is to introduce convergence theorems of some variable Krasnonsel skil-Mann iteration algorithms in Banach space and their applications which solve the multiple-set split feasibility problem. 1. Introduction The Krasnonsel skil-Mann K-M iteration algorithm 1 2 is used to solve a fixed point equation Tx X where T is a self-mapping of closed convex subset C of a Banach space X. The K-M .
