Mizoguchi-Takahashi局部收缩到Feng-Liu收缩
Mizoguchi-Takahashi local contractions to Feng-Liu contractions
摘要：
本文证明了在度量凸的完全度量空间上，任何一致局部Mizoguchi-Takahashi压缩实际上是Feng和Liu的集值压缩。通过一个例子证明了这一结果在任意度量空间上不成立。当度量空间是紧的时，我们证明了Mizoguchi-Takahashi局部压缩与Nadler局部压缩是等价的.此外，还建立了与不变最佳逼近有关的一个结果.
英文摘要：
In this article, we establish that any uniformly local Mizoguchi-Takahashi contraction is actually a set-valued contraction due to Feng and Liu on a metrically convex complete metric space. Through an example, we demonstrate that this result need not hold on any arbitrary metric space. Furthermore, when the metric space is compact, we derive that any Mizoguchi-Takahashi local contraction and Nadler local contraction are equivalent. Moreover, a result related to invariant best approximation is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
