tailieunhanh - Báo cáo hóa học: "Research Article The Solvability of a New System of Nonlinear Variational-Like Inclusions"

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 The Solvability of a New System of Nonlinear Variational-Like Inclusions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 609353 9 pages doi 2009 609353 Research Article The Solvability of a New System of Nonlinear Variational-Like Inclusions Zeqing Liu 1 Min Liu 1 Jeong Sheok Ume 2 and Shin Min Kang3 1 Department of Mathematics Liaoning Normal University . Box 200 Dalian Liaoning 116029 China 2 Department of Applied Mathematics Changwon National University Changwon 641-773 South Korea 3 Department of Mathematics and Research Institute of Natural Science Gyeongsang National University Jinju 660-701 South Korea Correspondence should be addressed to Jeong Sheok Ume jsume@ Received 23 November 2008 Accepted 1 April 2009 Recommended by Marlene Frigon We introduce and study a new system of nonlinear variational-like inclusions involving s- G n -maximal monotone operators strongly monotone operators n-strongly monotone operators relaxed monotone operators cocoercive operators Ằ -relaxed cocoercive operators Z y ọ -g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique associated with s- G n -maximal monotone operators and Banach contraction principle we demonstrate the existence and uniqueness of solution for the system of nonlinear variational-like inclusions. The results presented in the paper improve and extend some known results in the literature. Copyright 2009 Zeqing Liu 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 It is well known that the resolvent operator technique is an important method for solving various variational inequalities and inclusions 1-20 . In particular the generalized resolvent operator technique has been applied more and more and has also been improved intensively. For instance Fang and Huang 5 .