tailieunhanh - Báo cáo hóa học: " Research Article Iterative Approximation to Convex Feasibility Problems in 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 Iterative Approximation to Convex Feasibility Problems in Banach Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 46797 19 pages doi 2007 46797 Research Article Iterative Approximation to Convex Feasibility Problems in Banach Space Shih-Sen Chang Jen-Chih Yao Jong Kyu Kim and Li Yang Received 7 November 2006 Accepted 6 February 2007 Recommended by Billy E. Rhoades The convex feasibility problem CFP of finding a point in the nonempty intersection CiN 1Ci is considered where N 1 is an integer and each Ci is assumed to be the fixed point set of a nonexpansive mapping Ti E E where E is a reflexive Banach space with a weakly sequentially continuous duality mapping. By using viscosity approximation methods for a finite family of nonexpansive mappings it is shown that for any given contractive mapping f C C where C is a nonempty closed convex subset of E and for any given x0 e C the iterative scheme xn 1 P an 1 f xn 1 - an 1 Tn 1xn is strongly convergent to a solution of CFP if and only if an and xn satisfy certain conditions where an e 0 1 Tn Tn modN and P is a sunny nonexpansive retraction of E onto C. The results presented in the paper extend and improve some recent results in Xu 2004 O Hara et al. 2003 Song and Chen 2006 Bauschke 1996 Browder 1967 Halpern 1967 Jung 2005 Lions 1977 Moudafi 2000 Reich 1980 Wittmann 1992 Reich 1994 . Copyright 2007 Shih-Sen Chang 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 We are concerned with the following convex feasibility problem CFP N finding an x e Pl Ci where N 1 is an integer and each Ci is assumed to be the fixed point set of a nonex-pansive mapping Ti E E i 1 2 . N. There is a considerable investigation on CFP in the setting of Hilbert spaces which captures applications in various disciplines such as 2 Fixed Point Theory and Applications image .