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: Another weak convergence theorems for accretive mappings in banach spaces | Saejung et al. Fixed Point Theory and Applications 2011 2011 26 http content 2011 1 26 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Another weak convergence theorems for accretive mappings in banach spaces Satit Saejung Kanokwan Wongchan and Pongsakorn Yotkaew Correspondence saejung@. th Department of Mathematics Faculty of Science Khon kaen University Khon kaen 40002 Thailand SpringerOpen0 Abstract We present two weak convergence theorems for inverse strongly accretive mappings in Banach spaces which are supplements to the recent result of Aoyama et al. Fixed Point Theory Appl. 2006 Art. ID 35390 13pp. . 2000 MSC 47h1o 47J25. Keywords weak convergence theorem accretive mapping Banach space 1. Introduction Let E be a real Banach space with the dual space E . We write x x for the value of a functional x e E at x e E. The normalized duality mapping is the mapping J E 2E given by Jx x e E x x x 2 x 2 x e E . In this paper we assume that E is smooth that is lim .0 1 lx txIHIxl exists for all x y e E with x y 1. This implies that J is single-valued and we do consider the singleton Jx as an element in E . For a closed convex subset C of a smooth Banach space E the variational inequality problem for a mapping A C E is the problem of finding an element u e C such that Au J v u 0 for all v e C. The set of solutions of the problem above is denoted by S C A . It is noted that if C E then S C A A-10 x e E Ax 0 . This problem was studied by Stampac-chia see for example 1 2 . The applicability of the theory has been expanded to various problems from economics finance optimization and game theory. Gol shtein and Tret yakov 3 proved the following result in the finite dimensional space Rn. Theorem . Let a 0 and let A RN RN be an a-inverse strongly monotone mapping that is Ax - Ay X - y a Ax - Ay 2 for all x y e RN. Suppose that xn is a sequence in RN defined iteratively by x1 e RN and xn 1 xn nAxn .
