| 一类集值映射的半闭性及不动点的弱收敛 |
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| 引用本文： | 傅红卓,沈尧天.一类集值映射的半闭性及不动点的弱收敛[J].华南理工大学学报(自然科学版),2001,29(7):5-8. |
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| 作者姓名： | 傅红卓 沈尧天 |
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| 作者单位： | 华南理工大学应用数学系, |
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| 摘 要： | 讨论了一类集值映射的半闭性及不动点的弱收敛性，得到以下结论：若X为满足局部一致Opial条件的Banach空间，T为X中非弱紧凸子集上的连续集值渐近非扩张映射，则I－T在点0是半闭的.本文还分别讨论了满足局部一致Opial条件和满足一致Opial条件的Banach空间中这类映射的不动点的弱收敛，从而把单值渐近非扩张映射情形推广到集值渐近非扩张映射情形。
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| 关 键 词： | 集值映射 Banach空间 非扩张映射 半闭式 弱收敛性 不动点 Opial条件 |
| 文章编号： | 1000-565X(2001)07-0005-04 |
| 修稿时间： | 2000年11月30 |
Demiclosendess Principle of a Class of Multi_valued Mappings and Weak Convergence of the Fixed Point |
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| Fu Hong_zhuo,Shen Yao_tian.Demiclosendess Principle of a Class of Multi_valued Mappings and Weak Convergence of the Fixed Point[J].Journal of South China University of Technology(Natural Science Edition),2001,29(7):5-8. |
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| Authors: | Fu Hong_zhuo Shen Yao_tian |
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| Abstract: | This paper discusses the demiclosedness principle and weak convergence of the multi_valued asymptotically non_expansive mappings. It reaches the conclusion that if T is the continuous multi_valued asymptotically non_expansive mapping on the nonempty weakly compact convex subset of a Banach space satisfying the locally uniform Opial condition, then I-T is demiclosed at zero. The weak convergence of the fixed point of multi_valued asymptotically non_expansive mappings on the nonempty weakly compact convex subset of a Banach space satisfying locally uniform Opial condition or uniform Opial condition is also discussed. Some results of asymptotically non_expansive mappings are generalized. |
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| Keywords: | multi_valued mapping Banach space non_expansive mapping demiclosedness convergence |
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