2024, Vol. 9, Issue 5, Part B

In 2019, N. Manav and D. Turkoglu introduced a new class of generalized metric space called modular F metric space as a generalization of metric space. In this paper, we prove several fixed point theorems in the class of modular F-metric spaces which is a generalization of the metric spaces containing and extending as real world phenomena. We exemplify that all these results can be easily extended even if contraction condition exist on a subset of the space. Also, we extend classical known results for metric spaces Banach’s contraction principle, Kannan’s theorem, Edelstein’s theorem, Caristi’s theorem to the settings of modular F-metric spaces and lastly we deal with Reich’s type and Rhoades’ type theorems along with multivalued fixed point results which are also new in this more general setting. These generalizations present not only unify but generalize a large number of existing results which illustrate greater interest and usefulness of this new kind of generalized distance function over metric space (Modular F-metric) for solving problems in various branches of mathematics like differential equations, optimization theory etc. This paper opens up a whole network of challenging lines