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Symmetry 2018, 10(12), 767; https://doi.org/10.3390/sym10120767

Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations

1
Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 19 October 2018 / Revised: 8 November 2018 / Accepted: 21 November 2018 / Published: 18 December 2018
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Abstract

Using the concept of binary relation R , we initiate a notion of Θ R -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. View Full-Text
Keywords: complete metric space; ΘR-contractions; fixed point; binary relation complete metric space; ΘR-contractions; fixed point; binary relation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Al-Sulami, H.H.; Ahmad, J.; Hussain, N.; Latif, A. Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations. Symmetry 2018, 10, 767.

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