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báo cáo hóa học:" Research Article Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods"

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 Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 282171 18 pages doi 10.1155 2011 282171 Research Article Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods Lu Chuan Ceng 1 Yeong Cheng Liou 2 and Eskandar Naraghirad3 1 Department of Mathematics Shanghai Normal University Shanghai 200234 China 2 Department of Information Management Cheng Shiu University Kaohsiung 833 Taiwan 3 Department of Mathematics Yasouj University Yasouj 75914 Iran Correspondence should be addressed to Eskandar Naraghirad eskandarrad@gmail.com Received 18 August 2010 Accepted 23 September 2010 Academic Editor Jen Chih Yao Copyright 2011 Lu Chuan Ceng 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. The purpose of this paper is to introduce and investigate two kinds of iterative algorithms for the problem of finding zeros of maximal monotone operators. Weak and strong convergence theorems are established in a real Hilbert space. As applications we consider a problem of finding a minimizer of a convex function. 1. Introduction Let C be a nonempty closed and convex subset of a real Hilbert space H. In this paper we always assume that T C 2h is a maximal monotone operator. A classical method to solve the following set-valued equation 0 e Tx 1.1 is the proximal point method. To be more precise start with any point x0 e H and update xn 1 iteratively conforming to the following recursion xn e xn 1 AnTxn 1 Nn 0 1.2 where An c A to A 0 is a sequence of real numbers. However as pointed out in 1 the ideal form of the method is often impractical since in many cases to solve the problem 1.2 2 Fixed Point Theory and Applications exactly is either impossible or has the same difficulty as the original problem 1.1 . Therefore one of the most .