Contractive Operators in Relational Metric Spaces

Mihai Turinici ()
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Mihai Turinici: “A. I. Cuza” University

A chapter in Handbook of Functional Equations, 2014, pp 419-458 from Springer

Abstract: Abstract In Sect. 1, some fixed point results for altering contractive maps on (amorphous) metric spaces are given, extending the one due to Khan, Swaleh and Sessa [Bull Aust Math Soc 30:1–9, 1984],. In Sect. 2, a class of monotone contractions is analyzed, via coupled fixed point techniques, in the realm of quasi-ordered metric spaces. Note that, a highly unusual feature of the related fixed point techniques is that, in many cases with a practical relevance, no coupled starting point hypothesis for these operators is needed. Finally, in Sect. 3, some fixed point results are given for contractive operators acting on relational metric spaces.

Keywords: Metric space; Picard operator; Altering contractive map; Quasi-order; Monotone application; Ran–Reurings theorem; Coupled fixed point; Relation; Meir–Keeler contraction (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-1246-9_18

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