tailieunhanh - Báo cáo hóa học: " Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces | Homaeipour and Razani Fixed Point Theory and Applications 2011 2011 73 http content 2011 1 73 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces Simin Homaeipour 1 and Abdolrahman Razani1 2 Correspondence homaeipour_s@ department of Mathematics Faculty of Science Imam Khomeini International University . Box 34149-16818 Qazvin Iran Full list of author information is available at the end of the article Springer Abstract In this paper an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced and then weak and strong convergence theorems are proved. 2000 Mathematics Subject Classification 47H09 47H10 47J25. Keywords multi-valued mapping relatively nonexpansive fixed point iterative sequence 1 Introduction and preliminaries Let D be a nonempty closed convex subset of a real Banach space X. A single-valued mapping T D D is called nonexpansive if T x - T y x - y for all x y e D. Let N D and CB D denote the family of nonempty subsets and nonempty closed bounded subsets of D respectively. The Hausdorff metric on CB D is defined by H A1 A2 max sup d x A2 sup d y A1 x Ai y A2 for A1 A2 e CB D where d x A1 inf x - y y e A1 . The multi-valued map- ping T D CB D is called nonexpansive if H T x T y x - y for all x y e D. An element p e D is called a fixed point of T D N D respectively T D D if p e F T respectively T p p The set of fixed points of T is represented by F T . Let X be a real Banach space with dual X . We denote by J the normalized duality mapping from X to 2X defined by J x f e X xf II x 2 II ff 2 where . . denotes the generalized duality pairing. The Banach space X is strictly convex if x y 2 1 for all x y e X with x y 1 and x y. The Banach space X is uniformly convex if lim . . xn - yn 0 for any two sequences .