Fixed points of α-admissible Meir-Keeler contraction mappings on quasi-metric spaces

Abstract

We introduce α-admissible Meir-Keller and generalized α-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces. MSC: 47H10; 54C60; 54H25; 55M20

Equivalent Cauchy Sequences in q 1

“…Results in the (q 1 , q 2 )-Quasi Metric-Like Space. Many authors have given fixed-point theorems for the contractive function of the Mein-Keeler type in different spaces [23][24][25]. In this section, we acquire a fixed-point result related to the Mein-Keeler type contraction in the (q 1 , q 2 )-quasi metric-like space.…”

Some new fixed point theorems under $$(\mathcal {A},\mathcal {S})$$ ( A , S ) -contractivity conditions

“…In recent times, many fixed point results have been introduced using a function α : X × X → [0, ∞) rather than a binary relation (or a partial order) S. Some examples can be found on [1,3,11,22,23] and in references therein. We dedicate this subsection to translate our main results to such setting.…”

Remarks on the Quasi-Metric Extension of the Meir-Keeler Fixed Point Theorem With an Application to D3-Systems

“…The problem of extending the celebrated Meir-Keeler fixed point theorem to quasi-metric spaces has been recently discussed by Rachid, Mitrović, Parvaneh and Bagheri [5]. This problem was previously studied in [1] for T 1 quasi-metric spaces and in [8] for the general case. In particular, it was given in [8] an easy example of a Meir-Keeler map on a complete non-T 1 quasi-metric space that has no fixed points and also was obtained a fixed point theorem from which we immediately deduce that every Meir-Keeler map on a complete T 1 quasi-metric space has a unique fixed point (see Corollary 1 below).…”