Abstract
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. MSC:47H10, 47H07, 54H25.
Highlights
Introduction and preliminaries TheBanach contraction principle [ ] is a popular tool in solving existence problems in many branches of mathematics
We introduce an F-contraction with respect to a self-mapping on a metric space and obtain common fixed point results in an ordered metric space
We give some results on periodic point properties of a mapping and a pair of mappings in a metric space
Summary
Introduction and preliminaries TheBanach contraction principle [ ] is a popular tool in solving existence problems in many branches of mathematics (see, e.g., [ – ]). We introduce an F-contraction with respect to a self-mapping on a metric space and obtain common fixed point results in an ordered metric space. Let C(f , g) = {x ∈ X : fx = gx} (F(f , g) = {x ∈ X : x = fx = gx}) denote the set of all coincidence points (the set of all common fixed points) of self-mappings f and g.
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