无穷个m增生映射公共零点和变分不等式解的杂交迭代算法及计算试验（英文）  

Hybrid Iterative Scheme for Common Zeros of Infinite m-accretive Mappings and Solution of Variational Inequalities and Computational Experiments

作　　者：魏利[1] 张雅南[1] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《应用数学》2017年第1期179-187,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11071053);Natural Science Foundation of Hebei Province(A2014207010);Key Project of Science and Research of Hebei Educational Department(ZD2016024);Key Project of Science and Research of Hebei University of Economics and Business(2016KYZ07)

摘　　要：本文设计一种新的杂交迭代算法用以逼近变分不等式的解集和两组无穷个m增生映射零点集的公共元.充分利用距离投影映射和豫解式算子的性质,证明一个强收敛定理.利用Visual Basic 6编程,通过计算机运算,验证迭代算法的有效性.本文把有限个算子的研究推广到无限个算子的情形并把抽象理论与计算机编程结合在一起,推广和补充了近期的相关研究工作.One new hybrid iterative scheme for approximating the common element of the set of the solutions of variational inequalities and the sets of zeros of two infinite families of m-accretive mappings is presented. A strong convergence theorem is proved by using the properties of metric projection and resolvent sufficiently. The computational experiment to demonstrate the effectiveness of the proposed iterative schemes by using the codes of Visual Basic Six are conducted. The results in this paper extend the case of finite mappings to that of infinite mappings and combine the abstract results and the knowledge of computer programming, which extend and complement some of the recent corresponding work.

关 键 词：m-增生映射 投影映射 豫解式 k-Lipschitz连续映射 变分不等式 Visual Basin6编码 

分 类 号：O177.91[理学—数学]