Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle

Volume 9, Issue 3, pp 873--875 http://dx.doi.org/10.22436/jnsa.009.03.16

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Authors

Bessem Samet - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract

In this short note, we prove in few lines that Ran-Reurings fixed point theorem [A. C. M. Ran, M. C. B. Reurings, Proc. Amer. Math. Soc., 132 (2004), 1435-1443] is an immediate consequence of the famous Banach contraction principle.

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ISRP Style

Bessem Samet, Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 873--875

AMA Style

Samet Bessem, Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle. J. Nonlinear Sci. Appl. (2016); 9(3):873--875

Chicago/Turabian Style

Samet, Bessem. "Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 873--875

Keywords

Fixed point
Ran-Reurings fixed point theorem
Banach contraction principle.

MSC

47H10.

References

[1] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fundam. Math., 3 (1922), 133-181.

[2] R. Kannan, Some results on fixed points , Bull. Calcutta Math. Soc., 60 (1968), 71-76.

[3] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.