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Báo cáo hóa học: " The modified general iterative methods for nonexpansive semigroups in banach spaces†"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : The modified general iterative methods for nonexpansive semigroups in banach spaces† | Wangkeeree and Preechasilp Fixed Point Theory and Applications 2011 2011 76 http www.fixedpointtheoryandapplications.eom content 2011 1 76 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access The modified general iterative methods for nonexpansive semigroups in banach spaces 1 Rabian Wangkeeree and Pakkapon Preechasilp Correspondence rabianw@nu.ac. th Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Springer Abstract In this paper we introduce the modified general iterative approximation methods for finding a common fixed point of nonexpansive semigroups which is a unique solution of some variational inequalities. The strong convergence theorems are established in the framework of a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature. Mathematics Subject Classification 2000 47H05 47H09 47J25 65J15 Keywords nonexpansive semigroups strong convergence theorem Banach space common fixed point 1. Introduction Let C be a nonempty subset of a normed linear space E. Recall that a mapping T C C is called nonexpansive if Tx - Tyll x - yll Vx y e E. 1.1 We use F T to denote the set of fixed points of T that is F T x e E Tx x . A self mapping f E E is a contraction on E if there exists a constant a e 0 1 and x y e E such that II x - f y a x- y . 1.2 We use nE to denote the collection of all contractions on E. That is nE f f is a contraction on E . Here we consider a scheme for a semigroup of nonexpansive mappings. Let C be a closed convex subset of a Banach space E. Then a family 5 T s 0 s 1 of mappings of C into itself is called a nonexpansive semigroup on E if it satisfies the following conditions i T 0 x x for all x e C ii T s t T s T t for all s t 0 iii T s x - T s y x - y for all x y e C and s 0 iv for all x e C the mapping s T s x is continuous. We denote by F 5 the set of all common fixed points of 5 that is