关于均衡问题和两族半相对非扩张映射的混合迭代算法的强收敛定理.docVIP

关于均衡问题和两族半相对非扩张映射的混 合迭代算法的强收敛定理 步尚全 ，蔡钢 清华大学数学科学系，北京市　邮编 100084 摘要：本文引进一种混合迭代算法，在 Banach 框架下，找到了关于均衡问题解集和两族半相 对非扩张映射的公共不动点集的公共元，所得结果推广了许多必威体育精装版结果。 关键词：强收敛定理；混合算法；半非扩张映射；均衡问题 中图分类号： O177 Strong convergence by a hybrid projection algorithm for equilibrium problems and ?xed point problems of two ?nite families of hemi-relatively nonexpansive mappings Shangquan Bu , Gang Cai Department of Mathematical Sciences, Tsinghua University, Beijing City, 100084 Abstract: This purpose of this paper is to introduce a hybrid iterative scheme for ?nding a common element of the set of solutions of an equilibrium problem and the set of common ?xed points of two ?nite families of hemi-relatively nonexpansive mappings in the framework of Banach spaces.Our results improve and extend the recent ones announced by many others. Key words: Convergence theorem;Hybrid iterative method;Hemi-relatively nonexpansive mapping; Equilibrium problem. 0 Introduction Throughout the paper,let E be a real Banach space, E? the dual space of E.Let C be a nonempty closed convex subset of E. Recall that a mapping T : C → C is said to be nonexpansive if ∥T x ? T y∥ ≤ ∥x ? y∥ , ?x, y ∈ C.We denote by J the normalized duality 基金项目： Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(200800030059) 作者简介： 步尚全；男，教授，主要研究方向：泛函分析。通信作者：蔡钢 -1- {  2 2 }  , where ?., .? denotes the generalized duality pairing.It is well-known that if E? is strictly convex then J is single valued and if E is uniformly smooth then J is uniformly continuous on bounded subsets of E.Moreover,if E is a re?exive and strictly convex Banach space with a strictly convex dual,then J ?1 is single valued,one-to-one,surjective,and it is the duality mapping from E? into E and thus JJ ?1 = IE? and J ?1J = IE (see,[1,2]).We note that in a Hilbert space H,J is the identity operator. The equilibrium problem is to ?nd p ∈ C such that f(p, y) ≥ 0, ?y ∈ C.  (1.1) The set of solution of (1.1) is denoted by EP (f).G