tailieunhanh - Báo cáo hóa học: " Research Article Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems 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 Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 583082 19 pages doi 2008 583082 Research Article Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces Somyot Plubtieng and Kasamsuk Ungchittrakool Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Somyot Plubtieng somyotp@ Received 2 July 2008 Accepted 23 December 2008 Recommended by Hichem Ben-El-Mechaiekh The convex feasibility problem CFP of finding a point in the nonempty intersection nỉk Ci is considered where N 1 is an integer and the Ci s are assumed to be convex closed subsets of a Banach space E. By using hybrid iterative methods we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then we apply our results for solving convex feasibility problems in Banach spaces. Copyright 2008 S. Plubtieng and K. Ungchittrakool. 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 We are concerned with the convex feasibility problem CFP N finding an x e Q Ci where N 1 is an integer and C1 . CN are intersecting closed convex subsets of a Banach space E. This problem is a frequently appearing problem in diverse areas of mathematical and physical sciences. There is a considerable investigation on CFP in the framework of Hilbert spaces which captures applications in various disciplines such as image restoration 1-4 computer tomography 5 and radiation theraphy treatment planning 6 . In computer tomography with limited data in which an unknown image has to be reconstructed from a priori knowledge and from measured results each piece of information gives a constraint .

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