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.
Highlights
We introduce the notion of generalized F
It is widely known that the Banach contraction principle (BCP) [7] is the ...rst metric ...xed point theorem and one of the most powerful and versatile result in the ...eld of nonlinear analysis
It asserts that every contraction mapping on a complete metric space possesses a unique ...xed point
Summary
It is widely known that the Banach contraction principle (BCP) [7] is the ...rst metric ...xed point theorem and one of the most powerful and versatile result in the ...eld of nonlinear analysis. It asserts that every contraction mapping on a complete metric space possesses a unique ...xed point. C 2021 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics Another important generalization of the BCP was obtained by Alam and Imdad [1] in 2015. We apply our result to ...nd a solution of a class of non-linear matrix equations
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