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 New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 671754 24 pages doi 2011 671754 Research Article New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces Kamonrat Nammanee1 2 and Rabian Wangkeeree2 3 1 Department of Mathematics School of Science and Technology Phayao University Phayao 56000 Thailand 2 Centre of Excellence in Mathematics CHE Si Ayutthaya Road Bangkok 10400 Thailand 3 Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Rabian Wangkeeree rabianw@ Received 5 October 2010 Accepted 13 November 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 K. Nammanee and R. Wangkeeree. 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. We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others. 1. Introduction In recent years the existence of common fixed points for a finite family of nonexpansive mappings has been considered by many authors see 1-4 and the references therein . The well-known convex feasibility problem reduces to finding a point in the intersection of the fixed point sets of a family of nonexpansive mappings see 5 6 . The problem of finding an optimal point that minimizes a given cost function over the common set of fixed points of a family of nonexpansive mappings is of .
