On Ran–Reurings Fixed Point Theorem

Praveen Agarwal (), Mohamed Jleli and Bessem Samet
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Praveen Agarwal: Anand International College of Engineering, Department of Mathematics
Mohamed Jleli: King Saud University, Department of Mathematics, College of Sciences
Bessem Samet: King Saud University, Department of Mathematics, College of Sciences

Chapter Chapter 2 in Fixed Point Theory in Metric Spaces, 2018, pp 25-44 from Springer

Abstract: Abstract In order to study the existenceRan–Reurings fixed point theorem of solutions to a certain class of nonlinear matrix equationsMatrix equation, Ran and Reurings [38] established an extension of Banach contraction principleBanach contraction principle to metric spacesMetric space equipped with a partial orderPartial order. In this chapter, we present another proof of Ran–Reurings fixed point theoremRan–Reurings fixed point theorem using Banach contraction principle. Next, we present some applications of this result to the solvability of some classes of matrix equationsMatrix equation.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-2913-5_2

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DOI: 10.1007/978-981-13-2913-5_2

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