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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (4): 405-408    DOI: 10.3785/j.issn.1008-9497.2018.04.004
数学与计算机科学     
Lp空间中Lipschitz强单调算子方程解的迭代算法
杨延涛
延安大学 数学与计算机科学学院, 陕西 延安 716000
Iterative algorithms for the solutions of strongly monotone Lipschitz operator equations in Lp spaces
YANG Yantao
College of Mathematics and Computer Science, Yanan University, Yanan 716000, Shaanxi Province, China
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摘要： 设E=Lp（1 < p < ∞），A：E→E*为Lipschitz强单调算子.给出了Lp空间中Lipschitz强单调算子方程解的迭代构造算法，并证明由此算法构造的序列强收敛于Ax=0的唯一解，所得结果改进和推广了已有文献的相关结果.
关键词： 强单调算子;  Lipschitz;  算子方程;  迭代算法;  Lp空间    
Abstract: Let E=Lp(1 < p < ∞),and A:E→E* be a strongly monotone and Lipschitz operator.An iterative construction algorithm for the solutions of strongly monotone Lipschitz operator equations in Lp spaces is presented,and it is proved that the sequence constructed by the algorithm converges strongly to the unique solution of Ax=0. The results shown in this paper improve and generalize the recent ones in the literature.
Key words: strongly monotone operator    Lipschitz    operator equations    iterative algorithms    Lp spaces
收稿日期: 2017-06-12 出版日期: 2018-07-12
CLC:  O177.91  
基金资助: 国家自然科学基金资助项目（61751217）；陕西省教育厅2018年科研计划专项；延安市科技局2018年科研计划项目.
作者简介: 杨延涛(1982-),ORCID:http://orcid.org/0000-0001-7979-0612,男,硕士,讲师,主要从事非线性泛函分析研究,E-mail:yadxyyt@163.com.
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引用本文:

杨延涛. Lp空间中Lipschitz强单调算子方程解的迭代算法[J]. 浙江大学学报（理学版）, 2018, 45(4): 405-408.

YANG Yantao. Iterative algorithms for the solutions of strongly monotone Lipschitz operator equations in Lp spaces. Journal of Zhejiang University (Science Edition), 2018, 45(4): 405-408.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.04.004    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I4/405

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