| 张吉超,张文.强超弱紧生成Banach空间不动点性质[J].,2017,57(1):100-104 |
| 强超弱紧生成Banach空间不动点性质 |
| Fixed-point property of strongly super weakly compact generated Banach spaces |
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| DOI：10.7511/dllgxb201701014 |
| 中文关键词: 超弱紧集 不动点性质 Banach空间 |
| 英文关键词: super weakly compact set fixed-point property Banach space |
| 基金项目:国家自然科学基金资助项目(11471270)；福建省自然科学基金资助项目(2015J01022)；厦门大学校长基金资助项目(20720160010). |
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| 中文摘要: |
| 主要研究Banach空间的不动点性质,并给出一种全新的证明方法.首先利用超幂方法证明范数一致 G 光滑在凸集本身以及它的超幂上是相等的，然后利用反证法证明凸集在范数一致 G 光滑下对非扩张映射具有不动点性质,最后证明了每个强超弱紧生成的Banach空间在再赋范意义下满足每个弱紧凸集具有超不动点性质． |
| 英文摘要: |
| The fixed-point property of Banach space is studied and a new proof method is given. Firstly, the ultraproduct method is used to prove that the uniformly G -differentiable norms are equivalent under convex sets and its ultraproduct. Then, by means of counter-proof, it is proven that convex sets have the fixed-point property for nonexpansive mappings under the uniformly G -differentiable norm sense. Finally, it is shown that every strongly super weakly compact generated Banach space can be renormed so that every weakly compact convex set has super fixed-point property. |
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