Khantwal, Deepak2022-12-212022-12-212021https://doi.org/10.31801/cfsuasmas.793098http://hdl.handle.net/20.500.12575/86261In the present paper, we introduce the notion of generalize FR-contraction and establish some fixed point results for such mappings, which extend and generalize the result of Alam and Imdad (J. Fixed Point Theory & Appl., 17(4) (2015), 693-702), Sawangsup et al. (J. Fixed Point Theory, 2016 (2016), 1-15) and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not necessary condition for existence of fixed point in relational metric spaces. We also derive some N-order fixed point theorems from our main results. As an application of our main result, we find a solution of a certain class of nonlinear matrix equations.enFixed point, contraction mapping, binary relation, k-continuous mappingArticle7026316521303-5991