The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric space with probability measure (pq-space). Our motivation comes from biological sequence comparison: we show that many common similarity measures on biologica...

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].

We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the

This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, quasi-Sb-metric pseudo-Sb-metric quasi-N-metric space and pseudo space. We prove decomposition theorem fixed-point results in the setting of Further, we provide non-trivial examples to show validity introduced results. At end, solve an integral equation, system linear equations nonlinear fractional diff...

We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to R+ or to R , every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X . We construct an example of a complete path metric space quasi-isometric to R2 for which every degenerate triangle has one side wh...

We present a conjugate invariant method for completing any T0-quasi-metric space. The completion is built as an extension of the bicompletion of the original space. For balanced T0-quasi-metric spaces our completion yields up to isometry the completion due to Doitchinov. The question which uniformly continuous maps between T0-quasimetric spaces can be extended to the constructed completions lea...

A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...

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.