| 魏利,周海云.极大单调算子和非扩展映射的迭代收敛定理及其应用[J].数学研究及应用,2009,29(2):283~292 |
| 极大单调算子和非扩展映射的迭代收敛定理及其应用 |
| Iterative Convergence Theorems for Maximal Monotone Operators and Nonexpansive Mappings and Their Applications |
| 投稿时间：2007-03-09 修订日期：2007-09-07 |
| DOI：10.3770/j.issn:1000-341X.2009.02.011 |
| 中文关键词: 极大单调算子 迭代算法 强收敛 零点 不动点. |
| 英文关键词:maximal monotone operator iterative scheme strong convergence zero point fixed point. |
| 基金项目:国家自然科学基金(No.10771050). |
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| 中文摘要: |
| 在实一致光滑、一致凸Banach空间中，设计了两种新迭代格式用以逼近极大单调算子的零点集与一类广义非扩展映射的不动点集的公共元素. 得到了两个强收敛结论. 并讨论了它们在求解一类凸泛函最小值上的应用, 推广了以往的相关结论. |
| 英文摘要: |
| In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work. |
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