tailieunhanh - Báo cáo toán học: " Hierarchical convergence of an implicit doublenet algorithm for nonexpansive semigroups and variational inequality problems"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Hierarchical convergence of an implicit doublenet algorithm for nonexpansive semigroups and variational inequality problems | Yao et al. Fixed Point Theory and Applications 2011 2011 101 http content 2011 1 101 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Hierarchical convergence of an implicit doublenet algorithm for nonexpansive semigroups and variational inequality problems Yonghong Yao1 Yeol Je Cho2 and Yeong-Cheng Liou3 Correspondence yjcho@. kr department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 Republic of Korea Full list of author information is available at the end of the article Springer Abstract In this paper we show the hierarchical convergence of the following implicit doublenet algorithm 1 fẰ Xs t s tf Xs t 1 - t Xs t - fxÁXs t 1 - s T v Xs tdv Vs t e 0 1 Xs 0 where f is a p-contraction on a real Hilbert space H A H H is an a-inverse strongly monotone mapping and S T s s 0 H H is a nonexpansive semigroup with the common fixed points set Fix S 0 where Fix S denotes the set of fixed points of the mapping S and for each fixed t e 0 1 the net xs t converges in norm as s 0 to a common fixed point xt e Fix S of T s s 0and as t 0 the net xt converges in norm to the solution x of the following variational inequality í X e Fix S I Ax X X 0 Vx e Fix S . MSC 2000 49J40 47J20 47H09 65J15. Keywords fixed point variational inequality double-net algorithm hierarchical convergence Hilbert space 1 Introduction In nonlinear analysis a common approach to solving a problem with multiple solutions is to replace it by a family of perturbed problems admitting a unique solution and to obtain a particular solution as the limit of these perturbed solutions when the perturbation vanishes. In this paper we introduce a more general approach which consists in finding a particular part of the solution set of a given fixed point problem . fixed points which solve a variational inequality. More precisely the goal of this paper is to present a method for finding hierarchically a .