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Báo cáo hóa học: " Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities | Piri and Badali Fixed Point Theory and Applications 2011 2011 55 http www.fixedpointtheoryandapplications.eom content 2011 1 55 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities Hossein Piri and Ali Haji Badali Correspondence h. piri@bonabetu.ac.ir Department of Mathematics University of Bonab Bonab 5551761167 Iran Springer Abstract In this paper using strongly monotone and lipschitzian operator we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for b-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions we prove the strong convergence theorem for approximating a common element of the above two sets. Mathematics Subject Classification 2000 47H09 47H10 43A07 47J25 Keywords projection common fixed point amenable semigroup iterative process strong convergence variational inequality 1 Introduction Throughout this paper we assume that H is a real Hilbert space with inner product and norm are denoted by . . and . respectively and let C be a nonempty closed convex subset of H. A mapping T of C into itself is called nonexpansive if Tx - Ty x - y for all x y e H. By Fix T we denote the set of fixed points of T i.e. Fix T x e H Tx x it is well known that Fix T is closed and convex. Recall that a self-mapping f C C is a contraction on C if there exists a constant a e 0 1 such that fx - f y a x - y for all x y e C. Let B C H be a mapping. The variational inequality problem denoted by VI C B is to fined x e C such that Bx y x 0 1 for all y e C. The variational inequality problem has been extensively studied in literature. See for example 1 2 and the references .