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On Ran–Reurings Fixed Point Theorem

In: Fixed Point Theory in Metric Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Praveen Agarwal & Mohamed Jleli & Bessem Samet, 2018. "On Ran–Reurings Fixed Point Theorem," Springer Books, in: Fixed Point Theory in Metric Spaces, chapter 0, pages 25-44, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-2913-5_2
    DOI: 10.1007/978-981-13-2913-5_2
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