Relation theoretic metrical fixed point results for Suzuki type $\mathcal{Z_\mathcal{R}}$-contraction with an application

Abstract

In this paper, we introduce the concept of Suzuki type $\mathcal{Z_\mathcal{R}}$-contraction by unifying the definitions of Suzuki type $\mathcal{Z}$-contraction and $\mathcal{Z_\mathcal{R}}$-contraction and also provide examples to highlight the genuineness of our newly introduced contraction over earlier mentioned ones. Chiefly, we prove an existence and corresponding uniqueness fixed point results for Suzuki type $\mathcal{Z_\mathcal{R}}$-contraction employing an amorphous binary relation on metric spaces without completeness and also furnish an illustrative example to demonstrate the utility of our main results. Finally, we utilize our main results to discuss the existence and uniqueness of solutions of a family of nonlinear matrix equations.

Keywords

• fixed points
• suzuki type $\mathcal{z}_{\mathcal{r}}$-contraction
• simulation functions
• binary relations
• matrix equations