F-contraction on asymmetric metric spaces

Abstract

In this paper, we introduce the notion of an F-contraction in the setting of complete asymmetric metric spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature.

Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces

“…Further, their approach was used in the papers [1,2,8,10,11,12,13,14,15,16] to obtain various fixed point results, mostly for multivalued mappings. However, as we are going to show using the following result, most of the conditions used in all these articles are too strong.…”

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

“…In 2014, Minak et al [21] obtained result for generalized F -contractions including Ćirić type generalized F -contraction and almost Fcontraction on complete metric space. In 2017, Kumam et al [28] introduced the F -contraction in the setting of complete asymmetric metric spaces and extend several results. In 2018, Kadelburg and Radenović [16] obtained the result on concerning F -contraction in b-metric space.…”

Fixed point theorems for (phi,F)-contraction in generalized asymmetric metric spaces

“…A well known, several generalizations of standard metric spaces have appeared. In particular, asymmetric metric spaces were introduced by Wilson [21] and then studied by many authors (see [1,11,13,16]). In 2000, for the first time generalized metric spaces were introduced by Branciari [3], in such a way that triangle inequality is replaced by the quadrilateral inequality d(x, y) ≤ d(x, z) + d(z, u) + d(u, y) for all pairwise distinct points x, y, z and u.…”