Iterated function systems consisting of F-contractions

In this paper we consider a particular case of a contractive self-mapping on a complete metric space, namely the F -contraction introduced by Wardowski (Fixed Point Theory Appl. 87, 2012, doi:10.1186/1687-1812-2012-94), and provide some new properties of it. As an application, we investigate the ite...

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Bibliographic Details
Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2013; no. 1
Main Author Secelean, Nicolae-Adrian
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 08.11.2013
Subjects
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Topology
Hausdorff-Pompeiu metric
contraction
iterated function system
attractor
contractive map
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Summary:In this paper we consider a particular case of a contractive self-mapping on a complete metric space, namely the F -contraction introduced by Wardowski (Fixed Point Theory Appl. 87, 2012, doi:10.1186/1687-1812-2012-94), and provide some new properties of it. As an application, we investigate the iterated function systems (IFS) composed of F -contractions extending some fixed point results from the classical Hutchinson-Barnsley theory of IFS consisting of Banach contractions. Some illustrative examples are given. MSC: 28A80, 47H10, 54E50.
ISSN:1687-1812
1687-1812
DOI:10.1186/1687-1812-2013-277