and Applied Analysis 3 Clearly, every Menger PN-space is probabilistic metric space having a metrizable uniformity on X if supa<1T a, a 1. Definition 1.3. Let X,Λ, T be a Menger PN-space. i A sequence {xn} in X is said to be convergent to x in X if, for every > 0 and λ > 0, there exists positive integer N such that Λxn−x > 1 − λ whenever n ≥ N. ii A sequence {xn} in X is called Cauchy sequence ...

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. Corollary: the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group. Mathematics Subject Classification (2000): 20E42, 54F35, 20F67

The notion of copula was introduced by Sklar [24] who proved the theorem that now bears his name; it is commonly used in probability and statistics (see, for instance, [19, 22, 23]). Later, in order to characterize a class of operations on distribution functions that derive from operations on random variables defined on the same probability space, Alsina et al. [1] introduced the notion of quas...

In this paper, we establish some common fixed point theorems in fuzzy metric spaces for sequence of self mappings using implicit relation and the property (E.A). Our results extend, generalize and improve several results of metric spaces and menger spaces to fuzzy metric spaces.

1. A statistical metric space2 (briefly, an S M space) is a set 5 and a mapping $ from SXS into the set of distribution functions (i.e., real-valued functions of a real variable which are everywhere defined, nondecreasing, left-continuous and have inf 0 and sup 1). The distribution function *5(p, q) associated with a pair of points (p, q) in S is denoted by Fpq. The functions Fpq are assumed to...