Iterated function systems consisting of \(F\)-contractions. (English) Zbl 1405.28012
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 D. Wardowski [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)], 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 | Fractals |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
contractive map; \(F\)-contraction; iterated function system; attractor; Hausdorff-Pompeiu metricCitations:
Zbl 1310.54074References:
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