Relation-theoretic fixed point theorems under a new implicit function with applications to ordinary differential equations

In this paper, we introduce a new implicit function without any continuity requirement and utilize the same to prove unified relation-theoretic fixed point results. We adopt some examples to exhibit the utility of our implicit function. Furthermore, we use our results to derive some multidimensional fixed point results. Finally, as applications of our results, we study the existence and uniqueness of solution for a first-order ordinary differential equations.