Relation theoretic results via simulation function with applications

Document Type : Research Paper


1 Department of Mathematics H. N. B. Garhwal University, BGR Campus Pauri Garhwal-246001 Uttarakhand, India

2 Goverment Degree College Thatyur (Tehri Garhwal) Uttarakhand, India

3 Department of Mathematics, H.N.B. Garhwal university, Pauri Campus, Uttarakhand


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.