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Báo cáo hóa học: " Approximating fixed points for nonself mappings in CAT(0) spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Approximating fixed points for nonself mappings in CAT(0) spaces | Razani and Shabani Fixed Point Theory and Applications 2011 2011 65 http www.fixedpointtheoryandapplications.eom content 2011 1 65 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Approximating fixed points for nonself mappings in CAT 0 spaces Abdolrahman Razani and Saeed Shabani Correspondence s. shabani@srbiau.ac.ir Department of Mathematics Science and Research Branch Islamic Azad University Tehran Iran Springer Abstract Suppose K is a nonempty closed convex subset of a complete CAT 0 space X with the nearest point projection P from X onto K. Let T K X be a nonself mapping satisfying Condition E with F T x e K Tx x 0. Suppose xn is generated iteratively by x1 e K xn 1 P 1 - an xn anTP 1 - bn xn finTxnĩ n 1 where an and j8n are real sequences in e 1 - e for some e e 0 1 . Then xn A-converges to some point x in F T . This extends a result of Laowang and Panyanak Fixed Point Theory Appl. 367274 11 2010 for nonself mappings satisfying Condition E . Keywords CAT 0 spaces fixed point condition E nonself mappings 1 Introduction In 2010 Laowang and Panyanak 1 studied an iterative scheme and proved the following result let K be a nonempty closed convex subset of a complete CAT 0 space X the initials of term CAT are in honor of E. Cartan A.D. Alexanderov and V.A. Toponogov with the nearest point projection P from X onto K. Let T K X be a nonexpansive nonself mapping with nonempty fixed point set. If xn is generated iteratively by xi e K Xn 1 P 1 - an xn a TP 1 - Pn Xn PnTXn 1.1 where an and b are real sequences in e 1 - e for some e e 0 1 then xn is A-convergent to a fixed point of T. In this article this result is extended for nonself mappings satisfying Condition E . Let K be a nonempty subset of a CAT 0 space X and T K X be a mapping. A point x e K is called a fixed point of T if x Tx. We shall denote the fixed point set of T by F T . Moreover T is called nonexpansive if for each x y e K d Tx Ty d x y . In 2011 Falset et al. 2 introduced