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Generalized H-η-accretive operators in Banach spaces with application to variational inclusions
  • ISSN号：0253-4827
  • 期刊名称：《应用数学和力学：英文版》
  • 时间：0
  • 分类：O177.2[理学—数学;理学—基础数学] O177.91[理学—数学;理学—基础数学]
  • 作者机构：[1]Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China
  • 相关基金：Project supported by the National Natural Science Foundation of China （No. 10671135）, the Key Program of the National Natural Science Foundation of China （No. 70831005）, and the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20060610005）
作者： 罗雪萍[1], 黄南京[1]
关键词： Banach空间, 增生算子, 变分包含, 广义, LIPSCHITZ连续性, 应用, 迭代算法, 单调算子, generalized H-η-accretive operator, resolvent operator, variational inclusion, iterative algorithm, convergence
中文摘要：

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.

英文摘要：

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.

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期刊信息
  • 《应用数学和力学：英文版》
  • 主管单位:交通部
  • 主办单位:上海大学
  • 主编：周哲玮
  • 地址：上海市宝山区上大路99号上海大学122信箱
  • 邮编：200444
  • 邮箱：amm@department.shu.edu.cn
  • 电话：021-66135219 66165601
  • 国际标准刊号：ISSN：0253-4827
  • 国内统一刊号：ISSN：31-1650/O1
  • 邮发代号:
  • 获奖情况:
  • 上海市优秀科技期刊一等奖,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 美国数学评论（网络版）,波兰哥白尼索引,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库,日本日本科学技术振兴机构数据库,美国应用力学评论
  • 被引量:541