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: Regularization and iterative method for general variational inequality problem in hilbert spaces | Cho and Petrot Journal of Inequalities and Applications 2011 2011 21 http content 2011 1 21 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Regularization and iterative method for general variational inequality problem in hilbert spaces Yeol JE Cho 1 and Narin Petrot2 Correspondence narinp@ 2Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Full list of author information is available at the end of the article SpringerOpen0 Abstract Without the strong monotonicity assumption of the mapping we provide a regularization method for general variational inequality problem when its solution set is related to a solution set of an inverse strongly monotone mapping. Consequently an iterative algorithm for finding such a solution is constructed and convergent theorem of the such algorithm is proved. It is worth pointing out that since we do not assume strong monotonicity of general variational inequality problem our results improve and extend some well-known results in the literature. Keywords general variational inequality problem regularization inertial proximal point algorithm monotone mapping inverse strongly monotone mapping 1. Introduction It is well known that the ideas and techniques of the variational inequalities are being applied in a variety of diverse fields of pure and applied sciences and proven to be productive and innovative. It has been shown that this theory provides the most natural direct simple unified and efficient framework for a general treatment of a wide class of linear and nonlinear problems. The development of variational inequality theory can be viewed as the simultaneous pursuit of two different lines of research. On the one hand it reveals the fundamental facts on the qualitative aspects of the solutions to important classes of problems. On the other hand it also enables us to develop highly efficient and powerful
