Weak F-contractions and some fixed point results

In this paper we de ne weak F-contractions on a metric space into itself by extending F-contractions introduced by D. Wardowski (2012) and provide some xed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relation- ships between weak F-contractions and φ-contractions are highlighted. We also give some applications on fractal theory improving the classical Hutchinson-Barnsley s theory of iterated function systems. Some illus- trative examples are provided.