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Open AccessArticle

The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions

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Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
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Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 212; https://doi.org/10.3390/math8020212
Received: 16 November 2019 / Revised: 28 January 2020 / Accepted: 31 January 2020 / Published: 7 February 2020
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.
Keywords: F-contraction; fixed points; matrix equation; multi-valued mapping F-contraction; fixed points; matrix equation; multi-valued mapping
MDPI and ACS Style

Hussain, N.; Ali, G.; Iqbal, I.; Samet, B. The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions. Mathematics 2020, 8, 212.

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