tailieunhanh - Báo cáo hóa học: " WEAK CONVERGENCE OF AN ITERATIVE SEQUENCE FOR ACCRETIVE OPERATORS IN BANACH 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: WEAK CONVERGENCE OF AN ITERATIVE SEQUENCE FOR ACCRETIVE OPERATORS IN BANACH SPACES | WEAK CONVERGENCE OF AN ITERATIVE SEQUENCE FOR ACCRETIVE OPERATORS IN BANACH SPACES KOJI AOYAMA HIDEAKIIIDUKA AND WATARU TAKAHASHI Received 21 November 2005 Accepted 6 December 2005 Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u e C such that Au J v - u 0 for all v e C where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol shtein and Tret yakov in the Euclidean space to a Banach space. And using our theorem we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on. Copyright 2006 Koji Aoyama et al. 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 H be a real Hilbert space with norm II II and inner product let C be a nonempty closed convex subset of H and let A be a monotone operator of C into H. The variational inequality problem is formulated as finding a point u e C such that v - u Au 0 for all v e C. Such a point u e C is called a solution of the problem. Variational inequalities were initially studied by Stampacchia 13 17 and ever since have been widely studied. The set of solutions of the variational inequality problem is denoted by VI C A . In the case when C H VI H A A-10 holds where A-10 u e H Au 0 . An element of A-10 is called a zero point of A. An operator A of C into H is said to be inverse strongly monotone if there exists a positive real number a such that x - y Ax - Ay aflAx - Ay 2 for all x y e C see Browder and Petryshyn 5 Liu and Nashed 18 and Iiduka et al. 11 . For such a case A is said to be a-inverse strongly monotone. Let T be a nonexpansive mapping of C into itself. It is known