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
Abstract
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. 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 $G - {\rm{differentiable}}$ 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 $G - {\rm{differentiable}}$ 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.