Some new results in $ \mathcal{F} $-metric spaces with applications

Abstract

<abstract><p>In this research article, we give the notion of graphic $ F $-contraction in the setting of $ \mathcal{F} $-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally $ G $ -continuous graphic $ F $-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.</p></abstract>