tailieunhanh - Báo cáo hóa học: " Research Article Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-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 Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 59262 11 pages doi 2007 59262 Research Article Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces Rabian Wangkeeree Received 9 March 2007 Accepted 12 September 2007 Recommended by Wataru Takahashi Let E be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from E to E C a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E and T C - E a non-expansive nonself-mapping with F T 0. In this paper we study the strong convergence of two sequences generated by Xn 1 anX 1 - an 1 n 1 n 0 PT jXn and yn 1 1 n 1 nj 0P any 1 - an TP 1 yn for all n 0 where X x0 y y0 e C an is a real sequence in an interval 0 1 and P is a sunny non-expansive retraction of E onto C. We prove that xn and yn converge strongly to Qx and Qy respectively as n - TO where Q is a sunny non-expansive retraction of C onto F T . The results presented in this paper generalize extend and improve the corresponding results of Matsushita and Kuroiwa 2001 and many others. Copyright 2007 Rabian 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. 1. Introduction Let C be a nonempty closed convex subset of a Hilbert space E and let T be a nonexpan-sive mapping from C into itself that is II Tx - Ty II x - y II for all X y e C. In 1997 Shimizu and Takahashi 1 originally studied the convergence of an iteration process xn for a family of nonexpansive mappings in the framework of a Hilbert space. We restate the sequence xn as follows 1n xn 1 anx 1 - an 1 Tjxn for n 0 1 2 . 2 Fixed Point Theory and Applications where x0 x are all elements of C and an is an appropriate sequence in 0 1 . They proved that xn converges strongly to an .