Fixed and periodic points of generalized contractions in metric spaces

Abstract

Wardowski (Fixed Point Theory Appl. 2012:94, 2012, doi:10.1186/1687-1812-2012-94) introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalizes the Banach contraction principle. The aim of this paper is to introduce F-contractions with respect to a self-mapping on a metric space and to obtain common fixed point results. Examples are provided to support results and concepts presented herein. As an application of our results, periodic point results for the F-contractions in metric spaces are proved.