Common fixed point results on modular ℱ-metric spaces

Jleli and Samet[1] 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.