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Ran-Reurings fixed point results in ordered metric spaces. (English) Zbl 1239.54025

The first purpose of this very interesting paper is to show that the Ran-Reurings fixed point theorem [A. C. M. Ran and M. C. B. Reurings, Proc. Am. Math. Soc. 132, No. 5, 1435–1443 (2004; Zbl 1060.47056)] follows from Maia’s theorem [M. G. Maia, Rend. Sem. Mat. Univ. Padova 40, 139–143 (1968; Zbl 0188.45603)].
The second purpose is to give an extension of Maia’s theorem, which also includes some results on this topic (such as [J. J. Nieto, R. Rodriguez-Lopez, Order 22, No. 3, 223–239 (2005; Zbl 1095.47013)]).

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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