Iterated function systems consisting of F-contractions

By Nicolae-Adrian Secelean. Fixed Point Theory and Applications, 2013

237 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4fad6c5e30a074477d6db84c501160469588bb86

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In Geometry and Topology

Citations in the corpus

On Suzuki-Wardowski type fixed point theorems (2015, background): “On the other hand Secelean [23] proved the following lemma and replaced condition (F2) by an equivalent but a more simple condition (F2′ ).”
Common fixed point results for new Ciric-type rational multivalued F-contraction with an application (2018, background): “Afterward, Secelean [29] proved fixed point theorems regarding F -contraction by iterated function systems.”
F-contractions of Hardy–Rogers-type and application to multistage decision (2016, methodology): “The next theorem is inspired by Secelean [23].”
Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem (2017, background): “[22], Paesano and Vetro [26], Piri and Kumam [29], Secelean [31], and Sgroi and Vetro [32].”
Weak $F$-contractions and some fixed point results (2016, background): “in [17]).”