Implicit Contractive Maps in Ordered Metric Spaces

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

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 715-746 from Springer

Abstract: Abstract In Part 1, we show that most of the implicit contractions introduced by Wardowski [Fixed Point Theory Appl., 2012, 2012:94] are Matkowski type contractions. In Part 2, some limit type extensions are obtained for the fixed point result (involving implicit contractions) due to Altun and Simsek [Fixed Point Theory Appl., Volume 2010, Article ID 621469]. Moreover, the connections with a lot of related statements in the area due to Agarwal, El-Gebeily, and O’Regan [Appl. Anal. 87:109–116, 2008] are also discussed. Finally, in Part 3, a non-limit counterpart of these results is given, under the same general context.

Keywords: Metric space; Convergent and Cauchy sequence; Fixed point; Picard operator; Wardowski function; Limit and non-limit implicit contraction; Boyd-Wong and Matkowski admissible function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-06554-0_32

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