Common fixed points for set-valued generalized contractions on a metric space with graphical structure

Abstract

This manuscript deals with existence of common fixed points and coincidence points for set-valued generalized $f$-contraction in the setting of metric space having graphical structure. This result enables us to derive fixed points for set-valued generalized contractions on a metric space having directed graph. The main theorem generalizes and improves several results in the literature. An invariant approximation result on a normed linear space is derived from our main result. As an implementation of our main result, we deduce the sufficient criteria for occurrence of solution for the Caputo fractional differential equation.