tailieunhanh - Báo cáo hóa học: " Research Article A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings"

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 New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 64874 10 pages doi 2007 64874 Research Article A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings H. Y. Zhou Y. J. Cho and S. M. Kang Received 28 February 2007 Accepted 13 April 2007 Recommended by Nan-Jing Huang Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T1 T2 K E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences Kn ln c 1 00 limn okn 1 limn nln 1 F T1 n FT x E K T1x T2x x 0 respectively. Suppose that xn is a sequence in K generated iteratively by x1 E K xn 1 anxn hn PT1 nxn Yn PT2 nxn for all n 1 where an fin and yn are three real sequences in e 1 - e for some e 0 which satisfy condition an Pn Yn 1. Then we have the following. 1 If one of T1 and T2 is completely continuous or demicompact and y 00 1 kn - 1 w n 1 ln - 1 n then the strong convergence of xn to some q E F T1 n F T2 is established. 2 If E is a real uniformly convex Banach space satisfying Opial s condition or whose norm is Frechet differentiable then the weak convergence of xn to some q E F T1 n F T2 is proved. Copyright 2007 H. Y. Zhou 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 Let K be a nonempty closed convex subset of a real uniformly convex Banach space E. A self-mapping T K K is said to be nonexpansive if IIT x - T y II IIx - y II for all x y E K .A self-mapping T K K is called asymptotically nonexpansive if there exist sequences kn c 1 oo kn 1 as n n such that Tn x - Tn y II kn x - y II Vx y E K n 1. 2 Fixed Point Theory and Applications A self-mapping T K K is said to be uniformly L-Lipschitzian if there