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Báo cáo hóa học: " Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces"

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: Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces | Agarwal et al. Fixed Point Theory and Applications 2011 2011 31 http www.fixedpointtheoryandapplications.eom content 2011 1 31 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces Ravi P Agarwal1 Yeol JE Cho2 and Narin Petrot3 4 Correspondence narinp@nu.ac.th 3Department 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 In this paper the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties due to the presence of a proper convex lower semi-continuous function Ộ and a mapping g which appeared in the considered problem we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued mixed variational inequalities problems it is clear that it cannot be directly applied to the problems that we have considered in this paper because of Ộ and g. 2000 AMS Subject Classification 47H05 47H09 47J25 65J15. Keywords set-valued mixed variational inequalities maximal monotone operator resolvent operator strongly monotone operator Hausdorff metric 1. Introduction and preliminaries Let H be a real Hilbert space whose inner product and norm are denoted by and - respectively. Let CB H be the family of all nonempty closed and bounded sets in H. Let A B H CB H be nonlinear set-valued mappings g H H be a singlevalued mapping and ộ H - be a proper convex lower semi-continuous function on H. For each fixed positive real numbers p and h we consider the following so-called system of general nonlinear set-valued mixed variational inequalities problems Find x y e H u e Ay v