Weak F -contractions and some fixed point results

In this paper we define weak F-contractions on aý ýmetric space into itself by extending F-contractionsý ýintroduced by Dý. ýWardowski (2012) and provide some fixed pointý ýresults in complete metric spaces and in partially ordered complete ýgeneralized metric spacesý. ýSome relationships between weaký ýF-contractions and \Fi -contractions are highlightedý. ýWe also ýgive some applications on fractal theory improving the classicalý ýHutchinson-Barnsley's theory of iterated function systemsý. ýSomeý ýillustrative examples are providedý.