tailieunhanh - Báo cáo hóa học: " Fixed point theorems and Δ-convergence theorems for generalized hybrid mappings on CAT(0) 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: Fixed point theorems and Δ-convergence theorems for generalized hybrid mappings on CAT(0) spaces | Lin et al. Fixed Point Theory and Applications 2011 2011 49 http content 2011 1 49 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Fixed point theorems and A-convergence theorems for generalized hybrid mappings on CAT 0 spaces Lai-Jiu Lin 1 Chih-Sheng Chuang1 and Zenn-Tsun Yu2 Correspondence maljlin@. department of Mathematics National Changhua University of Education Changhua 50058 Taiwan Full list of author information is available at the end of the article Springer Abstract In this paper we introduce generalized hybrid mapping on CAT 0 spaces. The class of generalized hybrid mappings contains the class of nonexpansive mappings nonspreading mappings and hybrid mappings. We study the fixed point theorems of generalized hybrid mappings on CAT 0 spaces. We also consider some iteration processes for generalized hybrid mappings on CAT 0 spaces and our results generalize some results of fixed point theorems on CAT 0 spaces and Hilbert spaces. Keywords nonexpansive mapping fixed point generalized hybrid mapping CAT 0 spaces 1 Introduction Fixed point theory in CAT 0 spaces was first studied by Kirk 1 2 . He showed that every nonexpansive single-valued mapping defined on a bounded closed convex subset of a complete CAT 0 space always has a fixed point. Since then the fixed point theory for single-valued and multivalued mappings in CAT 0 spaces has been rapidly developed and many papers have appeared . see 3-6 and related references. Let X d be a metric space. A geodesic path joining x e X to y e X or more briefly a geodesic from x to y is a map c from a closed interval 0 I R to X such that c 0 x c l y and d c t c t t - t for all t t e 0 I . In particular c is an isometry and d x y I. The image a of c is called a geodesic or metric segment joining x and y. When it is unique this geodesic is denoted by x y . The space X d is said to be a geodesic space if every two points of X are .

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