In this paper, we prove results concerning the large scale geometry of connected, simply connected nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that there do not exist quasi-isometric embeddings of such a nilpotent Lie group into either a CAT0 metric space or an Alexandrov metric space. The main technical aspect of this work is the proof of a limited...

we obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of x.huang, c. zhu and x. wen.

in this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by george and veeramani cite{vee1}. some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. these results generalize several comparable results from the current literature. we also provide illustrative examples in support of ou...

CAT0 is an instructions environment for practicing basic skills of legal research: to use cases in arguments about a problem situation and to test a theory about a legal domain. Using the CAT0 tools, law students analyze a legal problem, frame queries of CATO’S database of legal cases, and judge how relevant the retrieved cases are to their developing argument or theory. CAT0 aids hming by maki...

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

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.

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...

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...