Relation-theoretic fixed point results for set-valued mappings via simulation functions with an Application

Abstract

In the present paper, we introduce a relatively new concept of set-valued $(\mathcal{Z},\mathcal{R})$-contractions and prove some fixed point results via simulation functions in metric spaces endowed with an amorphous binary relation. Illustrative examples are also furnished to exhibit the utility of our results proved herein. Finally, we obtain a solution for a class of nonlinear matrix equation to show the applicability of some of our obtain results.