^{}Department of Mathematics and Informatics Faculty of Sciences, Lucian Blaga University of Sibiu, Romania.

Receive Date: 24 October 2014,
Revise Date: 29 April 2015,
Accept Date: 29 April 2015

Abstract

In this paper we define weak $F$-contractions on a metric space into itself by extending $F$-contractions introduced by D. Wardowski (2012) and provide some fixed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relationships between weak $F$-contractions and $\varphi$-contractions are highlighted. We also give some applications on fractal theory improving the classical Hutchinson-Barnsley's theory of iterated function systems. Some illustrative examples are provided.

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