Relation theoretic (Θ,R) contraction results with applications to nonlinear matrix equations

Abstract

Using the concept of binary relation R, we initiate a notion of ΘR-contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.