tailieunhanh - Báo cáo hóa học: " Research Article Strong and Δ Convergence Theorems for Multivalued Mappings in CAT 0 Spa"

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 and Δ Convergence Theorems for Multivalued Mappings in CAT 0 Spa | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 730132 16 pages doi 2009 730132 Research Article Strong and A Convergence Theorems for Multivalued Mappings in CAT 0 Spaces W. Laowang and B. Panyanak Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand Correspondence should be addressed to B. Panyanak banchap@ Received 12 December 2008 Accepted 3 April 2009 Recommended by Nikolaos Papageorgiou We show strong and A convergence for Mann iteration of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT 0 space. The results we obtain are analogs of Banach space results by Song and Wang 2009 2008 . Strong convergence of Ishikawa iteration are also included. Copyright 2009 W. Laowang and B. Panyanak. 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 subset of a Banach space X. We shall denote by CB K the family of nonempty closed bounded subsets of K by PfK the family of nonempty bounded proximinal subsets of K and by K K the family of nonempty compact subsets of K. Let Hfi be the Hausdorff distance on CBfX that is H A B max sup dist a B supdist b A A B CB X aeA beB where dist a B inf d a b b e B is the distance from the point a to the set B. A multivalued mapping T K CBfX is said to be a nonexpansive if H Tx Ty d x y x y e K. A point x is called a fixed point of T if x e Tx. We denote by F T the set of all fixed points of T. 2 Journal of Inequalities and Applications In 2005 Sastry and Babu 1 introduced the Mann and Ishikawa iterations for multivalued mappings as follows let X be a real Hilbert space and T X P X be a multivalued mapping for which F T f 0. Fix p e F T and define A the sequence of Mann iterates by xo e X xn 1