Hilbert空间中涉及一类新的具误差迭代程序的平衡问题的黏性逼近法

Viscosity Approximation Methods for Equilibrium Problems in Hilbert Spaces Involving the New Iterative Process with Error

中文关键词:  黏性逼近法  平衡问题  非扩张映象.

英文关键词:viscosity approximation method  equilibrium problem  nonexpansive mapping.

中文摘要:

      本文在Hilbert空间引进了一类具误差项的迭代算法, 并利用黏性逼近法寻找平衡问题与非扩张映象的公共不动点,获得了该迭代序列强收敛的结果. 该结果推广了 S.Takahashi 和 W.Takahashi 2007年获得的所有结果. 同时, 本文也改进了该文献的某些方法.

英文摘要:

      In this paper, we introduce an iterative scheme with error by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. A strong convergence theorem is given, which generalizes all the results obtained by S.Takahashi and W.Takahashi in 2007. In addition, some of the methods applied in this paper improve those of S.Takahashi and W.Takahashi.