3rd International Conference of Mathematical Sciences (ICMS), İstanbul, Turkey, 4 - 08 September 2019, vol.2183
Jleli and Samet introduced a new concept, named a F-metric space, as a generalization of the notion of metric space. We define new generalization of modular metric space as modular F-metric space. We compare the topology produced by modular metric and by modular F-metric, then cover some useful properties of this topology for fixed point theorems for future studies. In the end, we prove Banach contraction principle for modular F-metric space.