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Báo cáo hóa học: " Research Article Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert 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: Research Article Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 547828 9 pages doi 10.1155 2010 547828 Research Article Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces Yuan Qing 1 Xiaolong Qin 1 Haiyun Zhou 2 and Shin Min Kang3 1 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China 2 Department of Mathematics Shijiazhuang Mechanical Engineering College Shijiazhuang 050003 China 3 Department of Mathematics Gyeongsang National University Jinju 660-701 Republic of Korea Correspondence should be addressed to Shin Min Kang smkang@gnu.ac.kr Received 16 July 2010 Revised 30 November 2010 Accepted 20 December 2010 Academic Editor Ljubomir B. Ciric Copyright 2010 Yuan Qing 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. Let H be a Hilbert space and C a nonempty closed convex subset of H. Let A C H be a maximal monotone mapping and f C C a bounded demicontinuous strong pseudocontraction. Let xt be the unique solution to the equation f x x tAx. Then xt is bounded if and only if xt converges strongly to a zero point of A as t OT which is the unique solution in A 1 0j where A-1 0 denotes the zero set of A to the following variational inequality f p - p y - p l 0 for all y e A-1 0 . 1. Introduction and Preliminaries Throughout this work we always assume that H is a real Hilbert space whose inner product and norm are denoted by and II II respectively. Let C be a nonempty closed convex subset of H and A a nonlinear mapping. We use D A and R A to denote the domain and the range of the mapping A. and denote strong and weak convergence respectively. Recall the following well-known definitions. 1 A mapping A C H is said to be monotone if Ax - Ay x - ỳ 0 x y e C. 1.1 2 The single-valued mapping A C H is maximal if the graph G A of A is not .