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Contraction Maps in Ordered Metrical Structures

In: Mathematics Without Boundaries

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  • Mihai Turinici

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

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.

Suggested Citation

  • Mihai Turinici, 2014. "Contraction Maps in Ordered Metrical Structures," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Mathematics Without Boundaries, edition 127, pages 533-575, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1124-0_17
    DOI: 10.1007/978-1-4939-1124-0_17
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