Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法

Viscosity Iterative Algorithms for a New Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces

本文在Hilbert空间上引入了一个新的粘性迭代算法,找到了关于两个逆强单调算子的变分不等式问题的解集与非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了强收敛定理,也给出了一个数值例子.所得结果改进了许多最新结果.

The aim of this paper is to introduce a new viscosity iterative algorithm for finding a common element of the set of solutions of a new variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of a nonexpansive mapping in Hilbert spaces.We give several strong convergence theorems under some suitable assumptions imposed on the parameters by using modified extragradient method.A numerical example is also given to support our main results.The results obtained in this paper extend and improve many recent ones.