Suzuki ψF-contractions and some fixed point results

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Resu...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2018, Vol.34 (1), p.93-102
Main Author: SECELEAN, NICOLAE-ADRIAN
Format: Article
Language:English
Online Access:Get full text
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Summary:The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2018.01.10