Fixed point theorems to generalize FR- contraction mappings with application to nonlinear matrix equations

Abstract

In the present paper, we introduce the notion of generalized F <contraction and establish some …xed point results for such mappings, which extend and generalize the result of Alam and Imdad [1], Sawangsup et al. [23] and many others. Our results reveal that the assumption of M -closedness of underlying binary relation is not a necessary condition for the existence of …xed points in relational metric spaces. We also derive some N -order …xed point theorems from our main results. As an application of our main result, we …nd a solution to a certain class of nonlinear matrix equations.