Structural Fixed Point Results in Metric Spaces

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

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 639-691 from Springer

Abstract: Abstract In Part 1, a class of anticipative contractions over quasi-ordered metric spaces is introduced and a corresponding lot of metrical fixed point theorems is formulated. The obtained facts include some well-known statements in the area due to Boyd and Wong or Matkowski, as well as a recent contribution due to Choudhury and Kundu (Demonstr Math 46:327–334, 2013). Further, in Part 2, a relative type version is given for the fixed point result in Leader (Math Jpn 24:17–24, 1979). Finally, in Part 3, an almost metric version is established for the 2008 Jachymski fixed point result (Proc Am Math Soc 136:1359–1373, 2008) involving Banach contractions over metric spaces endowed with a graph.

Keywords: Quasi-ordered metric space; (Globally strong) Picard operator; Fixed point; Admissible function; (Anticipative) Meir–Keeler contraction; Relative Leader contraction; Left-lsc function; Admissible point; Generalized (almost) metric space; Banach contraction; Equivalence class; Graph; Separation; Completeness (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_28

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DOI: 10.1007/978-3-319-31281-1_28

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