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

Abstract

In 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.

Keywords

• Fixed point
• contraction mapping
• binary relation
• k-continuous mapping

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