新路径定理和无穷个m增生算子的新迭代设计及计算试验（英文）  

A NEW PATH THEOREM AND A NEW ITERATIVE SCHEME FOR INFINITE M-ACCRETIVE OPERATORS AND COMPUTATIONAL EXPERIMENT

作　　者：魏利[1] 郑雅琴[2] 

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 [2]河北农业大学理学院,河北保定071001

出　　处：《数学杂志》2018年第2期269-284,共16页Journal of Mathematics

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);Science and Technology Foundation of Agricultural University of Hebei(LG201612)

摘　　要：本文研究了无穷个m增生算子公共零点的迭代构造问题.利用Banach极限的技巧和新路径收敛定理,证明了新构造的迭代序列强收敛到无穷个m增生算子的公共零点的结论,同时证明了这个公共零点还是一类变分不等式的解.利用Visual Basic 6编程,进行了计算试验用以验证迭代构造的合理性.迭代参数的限定条件更弱且采用了新的证明技巧,推广和补充了以往的相关研究成果.In this paper, we study the iterative construction of the common zero of infinite m- accretive operators. By using the technique of Banach limit and a new path convergence theorem, the iterative sequence is newly constructed proved to be strongly convergent to the common zero of infinite m-accretive operators, which is also the solution of one kind variational inequalities. The computational experiment is conducted by using codes of Visual Basic six to demonstrate the feasibility of the iterative scheme. The restrictions on the iterative parameters are weaker and some new techniques can be found, which extends and complements the corresponding work.

关 键 词：BANACH极限 增生算子 保核收缩映射 强正算子 Visual Basic 6 

分 类 号：O177.91[理学—数学]