Contraction Maps in Ordered Metrical Structures

Mihai Turinici ()
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Mihai Turinici: “A. I. Cuza” University, “A. Myller” Mathematical Seminar

A chapter in Mathematics Without Boundaries, 2014, pp 533-575 from Springer

Abstract: Abstract In Sect. 1, some basic fixed point results in (amorphous) metric spaces are given, including the ones due to Banach, Meir-Keeler, Boyd–Wong, and Matkowski. In Sect. 2, an enlargement of the fixed point theory above to the class of ordered metric spaces is performed. Moreover, we stress that the main statement in Ran and Reurings (Proc Am Math Soc 132:1435–1443, 2004) is reducible to Maia’s; and the one obtained by Nieto and Rodriguez-Lopez (Acta Math Sinica (English Series) 23:2205–2212, 2007) is nothing but a variant of Banach’s. Finally, in Sect. 3, the possibility of further extending these facts to the realm of almost partial metric spaces and Branciari metric spaces is discussed.

Keywords: Metric space; Convergent and cauchy sequence; (strong) Picard operator; Boyd-Wong and matkowski admissible function; Meir-Keeler contraction; Quasi-order; Ran-Reurings and nieto-lopez fixed point theorem; Almost partial and branciari metric (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-1124-0_17

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