The Study of Fixed Point Theorem over Modular F-metric Spaces - -, Sandeep; -, Vishal Saxena (International Journal For Multidisciplinary Research, 2024)
One of the most significant discoveries in the annals of mathematical history is Schauder's fixed-point theorem, which is generally recognized to be among the most important discoveries. The fact that the Brüwer fixed point hypothesis cannot be used in dimensions of space that are infinitely large is one of the most important discoveries in the history of mathematics. The facts that have been supplied make it feasible to claim that the great majority of them are of a topological nature. 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. It is generally agreed upon that this is one of the most significant discoveries that has been made in the subject of mathematics that has ever been produced. In this article, we study the basic structure of modular F-metric spaces and the concept of an equivalent relationship between modular F metric space and modular F metric bounded space. Moreover, we study the fixed point theorem (New version of Banach Contraction Principle) over modular F metric spaces. This is something that one would be able to predict occurring given the circumstances that are present. These results extend, broaden, and integrate many previously published results.