We study the notion of α-covering map with respect to certain subsets in metric spaces. Generalizing results from [1] we use this notion to give some coincidence theorems for pairs of single-valued and multivalued maps one of which is relatively α-covering while the other satisfies the Lipschitz condition. These assertions extend some classical contraction map principles. We define the notion of α-covering multimap at a point and give conditions under which the covering property of a multimap at each interior point of a set implies that it is covering on the whole set. As applications we consider the solvability of a system of inclusions and the existence of a positive trajectory for a semilinear feedback control system.

中文翻译：

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在度量空间和重合点中局部覆盖地图

我们研究了关于度量空间中某些子集的α覆盖图的概念。概括[1]的结果，我们使用此概念为单值和多值映射对提供了一些重合定理，其中一对相对覆盖，而另一个满足Lipschitz条件。这些主张扩展了一些经典的收缩图原理。我们在一个点上定义覆盖α的多图的概念，并给出条件，在该条件下，在集合的每个内部点处的多图的覆盖特性暗示该覆盖在整个集合上。作为应用程序，我们考虑了包含系统的可解性和半线性反馈控制系统的正轨迹的存在。