On a new generalization of metric spaces

In this paper, we introduce the $${\mathcal {F}}$$F-metric space concept, which generalizes the metric space notion. We define a natural topology $$\tau _{{\mathcal {F}}}$$τF in such spaces and we study their topological properties. Moreover, we establish a new version of the Banach contraction principle in the setting of $${\mathcal {F}}$$F-metric spaces. Several examples are presented to illustrate our study.