论文标题
关于在曲率正质量的空间上的典型非专用映射的固定点
On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature
论文作者
论文摘要
我们表明，在猫（$κ$）的一个小子集上典型的非专业映射（$κ$） - 空间是rakotch意义上的收缩。通常，我们的意思是，没有此属性的一组非专用映射是$σ$ - 孔子集，因此也是第一个Baire类别。此外，我们展示了指标空间，在非专业映射的空间中，严格的收缩并不致密。在某些情况下，我们表明所有连续的自我映射都具有固定点。
We show that the typical nonexpansive mapping on a small enough subset of a CAT($κ$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $σ$-porous set and therefore also of the first Baire category. Moreover, we exhibit metric spaces where strict contractions are not dense in the space of nonexpansive mappings. In some of these cases we show that all continuous self-mappings have a fixed point nevertheless.
