非扩张半群公共不动点与广义变分不等式解的迭代收敛性

Iterative Convergences of Common Fixed Points for Nonexpansive Semigroups and Solutions for Generalized Variational Inequalities

引入一种新的非扩张半群显式粘滞迭代算法,使用这种显式粘滞迭代算法,在较弱条件下,在Hilbert空间中建立了非扩张半群公共不动点集与具有α-可逆g-强单调映象的广义变分不等式解集的公共元素的强收敛定理,推广和改进了相关结果.

We introduce a new kind of explicit viscosity iterative algorithms for nonexpansive semigroups,and by using this kind of explicit viscosity iterative algorithms,the strong convergence theorems to find a common element of the set of common fixed points for nonexpansive semigroups and the set of solutions of generalized variational inequalities with α-inverse g-strongly monotone mapping in Hilbert spaces are established under the weaker condition.This paper extends and improves the corresponding results.