tailieunhanh - Báo cáo hóa học: "STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS"

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: STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS | STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS YONGFU SU AND XIAOLONG QIN Received 22 April 2006 Accepted 14 July 2006 Strong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups respectively. Our results extend and improve the recent ones announced by Nakajo Takahashi Kim Xu and some others. Copyright 2006 Y. Su and X. Qin. 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 and preliminary Let H be a real Hilbert space C a nonempty closed convex subset of H and T C C a mapping. Recall that T is nonexpansive if Tx- Ty x-yll Vx y e C and T is asymptotically nonexpansive if there exists a sequence kn of positive real numbers with limn TO kn 1 and such that Tnx- Tny kn x-yll Vn 1 x y e C. A point x e C is a fixed point of T provided Tx x. Denote by F T the set of fixed points of T that is F T x e C Tx x . Also recall that a family s T s I 0 s to of mappings from C into itself is called an asymptotically nonexpansive semigroup on C if it satisfies the following conditions i T 0 x x for all x e C ii T s 1 T s T t for all s 1 0 iii there exists a positive valued function L 0 to 1 to such that lims -to Ls 1 and IIT s x - T s y II Ls II x - y II for all x y e C and s 0 iv for all x e C s T s x is continuous. Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 96215 Pages 1-11 DOI FPTA 2006 96215 2 Nonexpansive mapping We denote by F S the set of all common fixed points of S that is F S Pl0 s TO F T s . It is known that F S is closed and convex. Construction of fixed point of non-expansive mapping is an important subject in the theory of nonexpansive mappings and finds applications