Abstract In this paper, the equivalence between multi-valued maps satisfying the Mizoguchi-Takahashi’s uniformly locally contractive condition and multi-valued maps satisfying the Nadler’s uniformly locally contractive condition is obtained on metrically convex space. We have provided examples to illustrate that this equivalence need not be true on any arbitrary metric space.

中文翻译：

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关于 Mizoguchi-Takahashi 局部收缩图与 Nadler 局部收缩图的等价性

摘要 本文在度量凸空间上得到了满足沟口-高桥一致局部收缩条件的多值映射与满足Nadler一致局部收缩条件的多值映射之间的等价性。我们已经提供了一些例子来说明这种等价性在任何任意度量空间上都不一定是真的。