For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

<p>When working with a metric space, we are dealing the additive group (R, +). Replacing +) an Abelian (G, ?), offers new structure of space. We call it G-metric space and induced topology is called topology. In this paper, studying spaces based on L-groups (i.e., partially ordered groups which lattices). Some results in obtained. The defined further studied for its topological properties...

in this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is riesz space valued. we prove some common fixed point theorems for three mappings in this space. obtained results extend and generalize well-known comparable results in the literature.

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

*Correspondence: [email protected] 1Department of Mathematics, Atilim University, İncek, Ankara 06836, Turkey Full list of author information is available at the end of the article Abstract The purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way. MSC: 46N40; 47H10; 54H25;...

and Applied Analysis 3 The following are examples of G-metric spaces. Example 1.8 see 7 . Let R, d be the usual metric space. Define Gs by Gs ( x, y, z ) d ( x, y ) d ( y, z ) d x, z , 1.4 for all x, y, z ∈ R. Then it is clear that R, Gs is a G-metric space. Example 1.9 see 7 . Let X {a, b}. Define G on X ×X ×X by G a, a, a G b, b, b 0, G a, a, b 1, G a, b, b 2 1.5 and extend G to X ×X ×X by us...

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...