tailieunhanh - báo cáo hóa học:" Research Article An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem "

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 An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 501293 12 pages doi 2010 501293 Research Article An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem Based on A n -Accretive Framework Hong Gang Li 1 An Jian Xu 1 and Mao Ming Jin2 1 Institute of Applied Mathematics Research Chongqing University of Posts and Telecommunications Chongqing 400065 China 2 Institute of Nonlinear Analysis Research Changjiang Normal University Fuling Chongqing 400803 China Correspondence should be addressed to Hong Gang Li lihg12@ Received 30 April 2010 Accepted 8 June 2010 Academic Editor Massimo Furi Copyright 2010 Hong Gang Li 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. A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of A n -accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to A n -accretive mapping due to Lan-Cho-Verma in Banach space. The result that sequence xn generated by the algorithm converges linearly to a solution of the nonlinear set-valued inclusions problem with the convergence rate 0 is proved. 1. Introduction The set-valued inclusions problem which was introduced and studied by Di Bella 1 Huang et al. 2 and Jeong 3 is a useful extension of the mathematics analysis. And the variational inclusion inequality is an important context in the set-valued inclusions problem. It provides us with a unified natural novel innovative and general technique to study a wide class of problems arising in different branches of mathematical and engineering sciences.