tailieunhanh - Báo cáo hóa học: " Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems | Yao et al. Fixed Point Theory and Applications 2011 2011 53 http content 2011 1 53 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems Yonghong Yao 1 Yeong-Cheng Liou2 Mu-Ming Wong3 and Jen-Chih Yao4 Correspondence mmwong@ department of Applied Mathematics Chung Yuan Christian University Chung Li 32023 Taiwan Full list of author information is available at the end of the article Springer Abstract In this paper we suggest a hybrid method for finding a common element of the set of solution of a monotone Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods extragradient method and CQ method. Under some mild conditions we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification 2000 47H05 47H09 47H10 47J05 47J25. Keywords variational inequality problem fixed point problems monotone mapping nonexpansive mapping extragradient method CQ method projection 1 Introduction Let H be a real Hilbert space with inner product Ộ and induced norm . Let C be a nonempty closed convex subset of H. Let A C H be a nonlinear operator. It is well known that the variational inequality problem VI C A is to find u e C such that Au v Ú 0 Vv e C. The set of solutions of the variational inequality is denoted by o. Variational inequality theory has emerged as an important tool in studying a wide class of obstacle unilateral and equilibrium problems which arise in several branches of pure and applied sciences in a unified and general framework. Several numerical methods have been developed for solving variational inequalities and related optimization problems see 1 1-25 and the references therein. Let us start with .