Relation theoretic contraction results in F-metric spaces

Abstract

Jleli and Samet in [M. Jleli, B. Samet, J. Fixed Point Theory Appl., 20 (2018), 20 pages] introduced a new metric space named as F-metric space. They presented a new version of the Banach contraction principle in the context of this generalized metric spaces. The aim of this article is to define relation theoretic contraction and prove some generalized fixed point theorems in F-metric spaces. Our results extend, generalize, and unify several known results in the literature.

Dass and Gupta's fixed point theorem in F-metric spaces

“…Later on [1] Alnaser et al defined relation theoretic contractions and extended Jleli et al [6] results and some known results of literature.…”

Some Generalized Fixed Point Results with Applications to Dynamic Programming

“…is F-convergent to ζ * . Afterwards, many researchers [2][3][4][5][6][7][8][9] worked in this space.…”

“…Recently, Jlei and Samet [1] initiated a generalized metric space named as F-metric space and showed a generalization of the Banach contraction principle. Meanwhile, researchers have picked keen interests in extending results in this generalized metric space; see for instance, [2][3][4][5]. In this paper, we define some generalized contractions and establish some results in the context of F-metric spaces.…”

New Fixed Point Theorems with Applications to Non-Linear Neutral Differential Equations

“…is F -convergent to u * . Furthermore, Alnaser et al [6] and Lateef et al [7] obtained the relation-theoretic contraction results and the fixed point theorems of Dass and Gupta, respectively, owing to the notion of F -metric spaces.…”