| 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 |
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| 引用本文： | 蔡钢.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[J].数学学报,2019,62(5):765-776. |
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| 作者姓名： | 蔡钢 |
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| 作者单位： | 重庆师范大学数学科学学院 重庆 401331 |
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| 基金项目： | 国家自然科学基金（11401063，11771063）；重庆市自然科学基金（cstc2017jcyjAX0006）；重庆市教委项目（KJ1703041）；重庆市高等学校青年骨干教师资助计划（020603011714）；重庆师范大学青年拔尖人才计划（02030307-00024） |
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| 摘 要： | 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.
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| 关 键 词： | 变分不等式 不动点 非扩张映射 强收敛 Hilbert空间 |
Viscosity Iterative Algorithms for a New Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces |
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| Gang CAI.Viscosity Iterative Algorithms for a New Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces[J].Acta Mathematica Sinica,2019,62(5):765-776. |
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| Authors: | Gang CAI |
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| Institution: | School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China |
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| Abstract: | 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. |
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| Keywords: | variational inequality fixed point nonexpansive mapping strong convergence Hilbert spaces |
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