Existence of solutions to a paratingent equation with delayed argument

Abstract

In this work we prove the existence of solutions of a class of paratingent equations with delayed argument, (Pt x) (t) ⊂ F([x]t) for t ≥ 0 with the initial condition x(t) = ξ(t) for t ≤ 0. We use a fixed point theorem to obtain a solution and then provide an estimate for the solution.