In this article, we present a completeness characterization of metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of metric spaces and (b) to establish completeness of a metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail.

中文翻译：

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度量空间的完备性与广义多值拟收缩的不动点

在本文中，我们介绍了 广义多值拟压缩不动点的存在性 本文的目的是双重的：（a）建立多值拟压缩不动点的存在性 度量空间和（b）建立a的完整性 度量空间，它是自然的一种拓扑性质，具有广义多值拟压缩不动点的存在。此外，我们的结果与可比较结果的比较表明，本文获得的结果改善并统一了适用于现有结果失败的情况的文献中的现有结果。