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Báo cáo hóa học: " APPROXIMATING ZERO POINTS OF ACCRETIVE OPERATORS WITH COMPACT DOMAINS IN GENERAL BANACH SPACES HIROMICHI MIYAKE AND WATARU TAKAHASHI "

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: APPROXIMATING ZERO POINTS OF ACCRETIVE OPERATORS WITH COMPACT DOMAINS IN GENERAL BANACH SPACES HIROMICHI MIYAKE AND WATARU TAKAHASHI | APPROXIMATING ZERO POINTS OF ACCRETIVE OPERATORS WITH COMPACT DOMAINS IN GENERAL BANACH SPACES HIROMICHI MIYAKE AND WATARU TAKAHASHI Received 2 July 2004 We prove strong convergence theorems of Mann s type and Halpern s type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces. 1. Introduction Let E be a real Banach space let C be a closed convex subset of E let T be a nonex-pansive mapping of C into itself that is II Tx - Ty II II x - y II for each x y e C and let A c E X E be an accretive operator. For r 0 we denote by Jr the resolvent of A that is Jr I rA -1. The problem of finding a solution u e E such that 0 e Au has been investigated by many authors for example see 3 4 7 16 26 . We know the proximal point algorithm based on a notion of resolvents of accretive operators. This algorithm generates a sequence xn in E such that x1 x e E and Xn 1 Jr x for n 1 2 . 1.1 where rn is a sequence in 0 to . Rockafellar 18 studied the weak convergence of the sequence generated by 1.1 in a Hilbert space see also the original works of Martinet 12 13 . On the other hand Mann 11 introduced the following iterative scheme for finding a fixed point of a nonexpansive mapping T in a Banach space x1 x e C and xn 1 anxn 1 - an Txn for n 1 2 . 1.2 where an is a sequence in 0 1 and studied the weak convergence of the sequence generated by 1.2 . Reich 17 also studied the following iterative scheme for finding a fixed point of a nonexpansive mapping T x1 x e C and xn 1 anx 1 - an Txn for n 1 2 . 1.3 Copyright 2005 Hindawi Publishing Corporation Fixed Point Theory and Applications 2005 1 2005 93-102 DOI 10.1155 FPTA.2005.93 94 Approximating zero points of accretive operators where an is a sequence in 0 1 see the original work of Halpern 6 . Wittmann 27 showed that the sequence generated by 1.3 in a Hilbert space converges strongly to the point of F T the set of fixed points of T which is the .