tailieunhanh - Báo cáo hóa học: " Research Article Strong Convergence of an Iterative Method for Inverse Strongly Accretive Operators"

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: Research Article Strong Convergence of an Iterative Method for Inverse Strongly Accretive Operators | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 420989 9 pages doi 2008 420989 Research Article Strong Convergence of an Iterative Method for Inverse Strongly Accretive Operators Yan Hao School of Mathematics Physics and Information Science Zhejiang Ocean University Zhoushan 316004 China Correspondence should be addressed to Yan Hao zjhaoyan@ Received 12 May 2008 Accepted 10 July 2008 Recommended by Jong Kim We study the strong convergence of an iterative method for inverse strongly accretive operators in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others. Copyright 2008 Yan Hao. 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 and preliminaries Let H be a real Hilbert space with norm - and inner product C a nonempty closed convex subset of H and A a monotone operator of C into H. The classical variational inequality problem is formulated as finding a point x e C such that y - x Ax 0 for all y e C. Such a point x e C is called a solution of the variational inequality . Next the set of solutions of the variational inequality is denoted by VI C A . In the case when C H VI H A A-10 holds where A-10 x e H Ax 0 . Recall that 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 aỊỊAx - Ay 2 for all x y e C see 1-4 . For such a case A is said to be a-inverse strongly monotone. 2 Journal of Inequalities and Applications Recall that T C C is nonexpansive if Tx - Tyll x - y for all x y C. It is known that if T is a nonexpansive mapping of C into itself then A I-T is 1 2-inverse strongly monotone and F T VI C A where F T denotes the set of fixed points of T. Let PC be the .