tailieunhanh - Báo cáo hóa học: "Research Article A Strong Convergence Theorem for a Family of Quasi-φ-Nonexpansive Mappings in a Banach Space"

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 A Strong Convergence Theorem for a Family of Quasi-φ-Nonexpansive Mappings in a Banach Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 351265 12 pages doi 2009 351265 Research Article A Strong Convergence Theorem for a Family of Quasi- -Nonexpansive Mappings in a Banach Space Haiyun Zhou1 and Xinghui Gao2 1 Department of Mathematics Shijiazhuang Mechanical Engineering College Shijiazhuang 050003 China 2 College of Mathematics and Computer Science Yanan University Yanan 716000 China Correspondence should be addressed to Haiyun Zhou witman66@ Received 26 May 2009 Revised 29 August 2009 Accepted 14 September 2009 Recommended by Nan-jing Huang The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi- -nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive strictly convex and smooth Banach spaces with the property K . The results of this paper improve and extend the results of S. Matsushita and W. Takahashi 2005 X. L. Qin and Y. F. Su 2007 and others. Copyright 2009 H. Zhou and X. Gao. 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 It is well known that in an infinite-dimensional Hilbert space the normal Mann s iterative algorithm has only weak convergence in general even for nonexpansive mappings. Consequently in order to obtain strong convergence one has to modify the normal Mann s iteration algorithm the so-called hybrid projection iteration method is such a modification. The hybrid projection iteration algorithm HPIA was introduced initially by Haugazeau 1 in 1968. For 40 years HPIA has received rapid developments. For details the readers are referred to papers 2-7 and the references therein. In 2005 Matsushita and Takahashi 5 proposed the following hybrid iteration method with generalized .