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Báo cáo hóa học: "A NEW SYSTEM OF GENERALIZED NONLINEAR RELAXED COCOERCIVE VARIATIONAL INEQUALITIES"

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: A NEW SYSTEM OF GENERALIZED NONLINEAR RELAXED COCOERCIVE VARIATIONAL INEQUALITIES | A NEW SYSTEM OF GENERALIZED NONLINEAR RELAXED COCOERCIVE VARIATIONAL INEQUALITIES KE DING WEN-YONG YAN AND NAN-JING HUANG Received 21 November 2004 Revised 13 April 2005 Accepted 28 June 2005 We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the convergence of iterative sequences generated by the algorithm. We also study the convergence and stability of a new perturbed iterative algorithm for approximating the solution. Copyright 2006 Ke Ding 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. 1. Introduction Variational inequality problems have various applications in mechanics and physics optimization and control linear and nonlinear programming economics and finance transportation equilibrium and engineering science and so forth. Consequently considerable attention has been devoted to the study of the theory and efficient numerical methods for variational inequality problems see e.g. 2-17 and the references therein . In 15 Verma introduced a new system of nonlinear strongly monotone variational inequalities and studied the approximate of this system based on the projection method and in 16 Verma discussed the approximate solvability of a system of nonlinear relaxed cocoercive variational inequalities in Hilbert spaces. Recently Kim and Kim 14 introduced and studied a system of nonlinear mixed variational inequalities in Hilbert spaces and obtained some approximate solvability results. In the recent paper 6 Cho et al. introduced and studied a new system of nonlinear .