A new generalization of the metric space notion, named \({\mathcal {F}}\)-metric space, was given in [M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), no. 3, Art. 128, 20 pp.]. In this paper, we investigate some properties of \({\mathcal {F}}\)-metric spaces. A simple proof is given to show that the natural topology induced by an \({\mathcal {F}}\)-metric is metrizable. We present a method to construct s-\(\hbox {relaxed}_{{p}}\) spaces and, therefore, \({\mathcal {F}}\)-metric spaces from bounded metric spaces. We give some results that reveal differences between metric and \({\mathcal {F}}\)-metric spaces. In particular, we show that the ordinary open and closed balls in \({\mathcal {F}}\)-metric spaces are not necessarily topological open and closed, respectively. This answers a question posed implicitly in the quoted paper. We also show that \({\mathcal {F}}\)-metrics are not necessarily jointly continuous functions. Despite some topological differences between metrics and \({\mathcal {F}}\)-metrics, we show that the Nadler fixed point theorem and, therefore, the Banach contraction principle in the frame of \({\mathcal {F}}\)-metric spaces can be reduced to their original metric versions. This reduction even happens when the Schauder fixed point theorem is investigated in \({\mathcal {F}}\)-normed spaces structure. By applying the given technique in this paper, it turns out that some nonlinear \({\mathcal {F}}\)-metric contractions and, therefore, the related \({\mathcal {F}}\)-metric fixed point results can naturally be reduced to their metric versions. In addition, the same happens for some topological fixed point results.

度量空间概念的新概括称为\（{\ mathcal {F}} \） -度量空间，在[M. Jleli，B。Samet，关于度量空间的新概括，J。不动点理论应用。20（2018），否 3，艺术。128，20 pp。]。在本文中，我们研究了\（{\ mathcal {F}} \） -度量空间的一些属性。给出了一个简单的证明，以证明由\（{\ mathcal {F}} \）度量引发的自然拓扑是可度量的。我们提出一种方法来构造s - \（\ hbox {relaxed} _ {{p}} \）空间，并因此从有界度量空间构造\（{\ mathcal {F}} \） -度量空间。我们给出一些结果来揭示度量标准与\（{\ mathcal {F}} \）之间的差异度量空间。特别地，我们表明\（{\ mathcal {F}} \） -度量空间中的普通开球和闭球不必分别是拓扑上的开和闭。这回答了引文中隐含地提出的一个问题。我们还表明\（{\ mathcal {F}} \）-度量不一定是联合连续函数。尽管度量和\（{\ mathcal {F}} \）- metrics之间在拓扑上存在一些差异，但我们显示了Nadler不动点定理，因此，在\（{\ mathcal {F}}框架中的Banach压缩原理\） -度量标准空间可以减少到其原始度量标准版本。当在\（{\ mathcal {F}} \）中研究Schauder不动点定理时，甚至会发生这种减少。规范的空间结构。通过应用本文中的给定技术，结果证明了一些非线性\（{\ mathcal {F}} \） -度量收缩，因此，相关的\（{\ mathcal {F}} \） -metric不动点结果自然可以减少到其公制版本。此外，某些拓扑固定点结果也会发生同样的情况。