tailieunhanh - Báo cáo hóa học: "Research Article Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces"

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 Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 21972 18 pages doi 2007 21972 Research Article Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces Fumiaki Kohsaka and Wataru Takahashi Received 7 November 2006 Accepted 12 November 2006 Recommended by Ravi P. Agarwal Using the convex combination based on Bregman distances due to Censor and Reich we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next using this operator we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces. Copyright 2007 F. Kohsaka and W. Takahashi. 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 H be a Hilbert space and let Ci I m I be a family of closed convex subsets of H such that F Pl 1 Ci is nonempty. Then the problem of image recovery is to find an element of F using the metric projection Pi from H onto Ci i 1 2 . m where Pi x argmin IIy - x yECi for all x E H. This problem is connected with the convex feasibility problem. In fact if gi m 1 is a family of continuous convex functions from H into R then the convex feasibility problem is to find an element of the feasible set m P x E H gi x 0 . i 1 We know that each Pi is a nonexpansive retraction from H onto Ci that is Pix - Pi-y x- y II 2 Fixed Point Theory and Applications for all x y e H and P2 Pi. Further it holds that F n 1 F Pi where F Pi denotes the set of all fixed points of Pi i 1 2 . m . Thus the problem of image recovery in the setting of Hilbert spaces is a common fixed .