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 A General Projection Method for a System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 45398 9 pages doi 2007 45398 Research Article A General Projection Method for a System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces Meijuan Shang Yongfu Su and Xiaolong Qin Received 2 June 2007 Accepted 19 July 2007 Recommended by Saburou Saitoh We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results include the previous results as special cases extend and improve the main results of R. U. Verma 2004 S. S. Chang et al. 2007 Z. Y. Huang and M. A. Noor 2007 and many others. Copyright 2007 Meijuan Shang 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 and preliminaries Variational inequalities introduced by Stampacchia 1 in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied sciences and have witnessed an explosive growth in theoretical advances and algorithmic development see 1-11 and references therein. It is well known that the variational inequality problems are equivalent to the fixed point problems. This alternative equivalent formulation is very important from the numerical analysis point of view and has played a significant part in several numerical methods for solving variational inequalities and complementarity see 2 4 . In particular the solution of the variational inequalities can be computed using the iterative projection methods. It is well known that the convergence of the projection method requires the operator T to be strongly monotone and Lipschitz continuous. Gabay 5 has shown that the convergence of a projection method can be proved .
