Some Interesting Results on F -metric Spaces

Abstract

In this manuscript, we claim that the newly introduced F -metric spaces are Hausdorff and also first countable. We investigate some interrelations among the Lindelofness, separability and second countability axiom in the setting of F -metric spaces. Moreover, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial examples. Finally, we raise an open problem regarding the structure of an open set in this setting.