Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces | Wang and Chen Fixed Point Theory and Applications 2011 2011 63 http content 2011 1 63 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces Yaqin Wang1 2 and Rudong Chen3 Correspondence wangyaqin0579@ department of Mathematics Shaoxing University Shaoxing 312000 China Full list of author information is available at the end of the article Springer Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. Fixed Point Theory Appl doi 2011 180534 2011 and Lu et al. Nonlinear Anal 71 3-4 1032-1041 2009 . 2000 Mathematics subject classification 47H05 47H09 65J15 Keywords hybrid method accretive operator variational inequality pseudocontraction 1. Introduction Throughout this paper we always assume that E is a real Banach space is the dual pair between E and E and 2E denotes the family of all the nonempty subsets of E. Let C be a nonempty closed convex subset of E and T C E be a nonlinear mapping. Denote by Fix T the set of fixed points of T that is Fix T x e C Tx x . The generalized duality mapping J E 2E is defined by J x f e E xf x f x Vx e E. In the sequel we shall denote the single-valued duality mapping by j. When xn is a sequence in E xn x xn - x xn H x will denote strong respectively weak and weak convergence of the sequence xn to x. A mapping T with domain D T and range R T in E is called pseudocontractive if the inequality x - y x - y t I - T x - I - T y holds for each x
