希尔伯特空间中关于广义均衡问题和有限组非扩张映像的不动点的强收敛定理

Strong Convergence Theorem for a Generalized Equilibrium Problem and Fixed Points of a Finite Family of Nonexpansive Mappings in A Hilbert Space

在希尔伯特空间,我们引入一个新的迭代序列来逼近广义均衡问题和有限组扩张映像的不动点的公共元素.相应推广了Satoru Takahashi,Wararu Takahashi[Strong convergence theorem for a generalized equilibrium prob-lem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)0250-1033]

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of a generalized equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space.This main theorem extends a recent result of Satoru Takahashi and WararuTakahashi[Satoru Takahashi,Wataru Takahashi,Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69（2008）1025-1033].