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 Approximate Fixed Points for Nonexpansive and Quasi-Nonexpansive Mappings in Hyperspaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 520976 16 pages doi 2009 520976 Research Article Approximate Fixed Points for Nonexpansive and Quasi-Nonexpansive Mappings in Hyperspaces Zeqing Liu 1 Jeong Sheok Ume 2 and Shin Min Kang3 1 Department of Mathematics Liaoning Normal University Dalian Liaoning 116029 China 2 Department of Applied Mathematics Changwon National University Changwon 641-773 South Korea 3 Department of Mathematics Research Institute of Natural Science Gyeongsang National University Chinju 660-701 South Korea Correspondence should be addressed to Jeong Sheok Ume jsume@ Received 9 May 2009 Accepted 14 December 2009 Recommended by W. A. Kirk This paper provides a few convergence results of the Ishikawa iteration sequence with errors for nonexpansive and quasi-nonexpansive mappings in hyperspaces. The results presented in this paper improve and generalize some results in the literature. Copyright 2009 Zeqing Liu 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 and Preliminaries Browder 1 and Kirk 2 established that a nonexpansive mapping T which maps a closed bounded convex subset C of a uniformly convex Banach space into itself has a fixed point in C. Since then many researchers have studied under various conditions the convergence of the Mann and Ishikawa iteration methods dealing with nonexpansive and quasi-nonexpansive mappings see 3-11 and the references therein . Rhoades 9 pointed out that the Picard iteration schemes for nonexpansive mappings need not converge. Senter and Dotson 10 obtained conditions under which the Mann iteration schemes generated by nonexpansive and quasi-nonexpansiv mappings in uniformly convex Banach spaces converge to fixed points of these mappings respectively. Ishikawa
