Abstract
Abstract In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.
Highlights
In recent times, one of the branches of fixed point theory that has attracted much attention is the field devoted to studying this kind of results in the setting of partially ordered metric spaces
In [ ], the authors introduced the notion of mixed monotone property, which has been one of the most usual hypotheses in this kind of results
3.2 Coincidence point theorems using (g, M, )-contractions of the first kind we present the kind of contractions we will use
Summary
One of the branches of fixed point theory that has attracted much attention is the field devoted to studying this kind of results in the setting of partially ordered metric spaces. We present some coincidence point theorems in the framework of quasimetric spaces under very general conditions which can be extended to the coupled case and can be applied to mappings that have not necessarily the mixed monotone property. Let (X, q) be a quasi-metric space, let T, g : X → X be two mappings, and let M ⊆ X be a g-closed, nonempty subset of X such that (X, q, M) is regular.
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