New coincidence point results for generalized graph-preserving multivalued mappings with applications

Abstract

Abstract This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms). An example and some corollaries are derived to strengthen our main theoretical results. We end the manuscript with two important applications, one of them is interested in finding a solution to the system of nonlinear integral equations (nie) and the other one relies on the existence of a solution to fractional integral equations (fie).

Keywords

• Coincidence point
• Directed graph
• Fractional integral equation
• b-metric space
• Set valued graph-preserving mappings