tailieunhanh - Báo cáo hóa học: "A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems"

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: A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems | Jung Journal of Inequalities and Applications 2011 2011 51 http content 2011 1 51 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access A general composite iterative method for generalized mixed equilibrium problems variational inequality problems and optimization problems Jong Soo Jung Correspondence jungjs@mail. Department of Mathematics Dong-A University Busan 604-714 Korea Springer Abstract In this article we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions which solves a certain optimization problem. The results of this article substantially improve develop and complement the previous well-known results in this area. 2010 Mathematics Subject Classifications 49J30 49J40 47H09 47H10 47J20 47J25 47J05 49M05. Keywords generalized mixed equilibrium problem fixed point nonexpansive mapping inverse-strongly monotone mapping variational inequality optimization problem metric projection strongly positive bounded linear operator 1 Introduction Let H be a real Hilbert space with inner product and induced norm . Let C be a nonempty closed convex subset of H and S C C be a self-mapping on C. Let us denote by F S the set of fixed points of S and by PC the metric projection of H onto C. Let B C H be a nonlinear mapping and ộ C R be a function and 0 be a bifunction of C X C into R where R is the set of real numbers. Then we consider the following generalized mixed equilibrium problem of finding x e C such that x y Bx y x ự y ự x 0 Vy e C