Relation theoretic results via simulation function with applications

Abstract

We introduce '{C}iri'{c} type $ mathcal{Z}_mathcal{R} $-contraction to investigate the existence of single fixed point under a binary relation. In the sequel we demonstrate that variety of contractions are obtained as consequences of our contraction. Also we provide illustrative examples to demonstrate the significance of '{C}iri'{c} type $ mathcal{Z}_mathcal{R} $-contraction in the existence of fixed point for discontinuous map via binary relation. The paper is concluded by applications to solve an integral equation and a nonlinear matrix equation.