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 General System of A-Monotone Nonlinear Variational Inclusions Problems with Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 364615 13 pages doi 2009 364615 Research Article General System of A-Monotone Nonlinear Variational Inclusions Problems with Applications Jian-Wen Peng1 and Lai-Jun Zhao2 1 College of Mathematics and Computer Science Chongqing Normal University Chongqing 400047 China 2 Management School Shanghai University Shanghai 200444 China Correspondence should be addressed to Lai-Jun Zhao zhao_laijun@ Received 25 September 2009 Accepted 2 November 2009 Recommended by Vy Khoi Le We introduce and study a new system of nonlinear variational inclusions involving a combination of A-Monotone operators and relaxed cocoercive mappings. By using the resolvent technique of the A-monotone operators we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions. The results in this paper unify extend and improve some known results in literature. Copyright 2009 . Peng and . Zhao. 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 Recently Fang and Huang 1 introduced a new class of H-monotone mappings in the context of solving a system of variational inclusions involving a combianation of H-monotone and strongly monotone mappings based on the resolvent operator techniques. The notion of the H -monotonicity has revitalized the theory of maximal monotone mappings in several directions especially in the domain of applications. Verma 2 introduced the notion of A-monotone mappings and its applications to the solvability of a system of variational inclusions involving a combination of A-monotone and strongly monotone mappings. As Verma point out the class of A-monotone mappings generalizes H-monotone mappings. On the top
