Motivated by the Category Embedding Theorem, as applied to convergent automorphisms [BOst11], we unify and extend the multivariate regular variation literature by a reformulation in the language of topological dynamics. Here the natural setting are metric groups, seen as normed groups (mimicking normed vector spaces). We brie‡y study their properties as a preliminary to establishing that the Un...

Hard metrics are the class of extremal metrics with respect to embedding into Euclidean spaces: they incur Ω(logn) multiplicative distortion, which is as large as it can possibly get for any metric space of size n. Besides being very interesting objects akin to expanders and good error-correcting codes, and having a rich structure, such metrics are important for obtaining lower bounds in combin...

We present a constant-factor approximation algorithm for computing an embedding of the shortest path metric of an unweighted graph into a tree, that minimizes the multiplicative distortion.

In this paper, we prove some common fixed point theorems for weakly compatible mappings satisfying binary operations in multiplicative metric spaces. AMS Subject Classification: 47H10, 54H25

This paper discusses the instability of eleven nonlinear state space models that underly exponential smoothing. Hyndman et al. (2002) proposed a framework of 24 state space models for exponential smoothing, including the well-known simple exponential smoothing, Holt’s linear and Holt-Winters’ additive and multiplicative methods. This was extended to 30 models with Taylor’s (2003) damped multipl...

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

Let ({1, 2, . . . , n}, d) be a metric space. We analyze the expected value and the variance of ∑bn/2c i=1 d(π(2i − 1),π(2i)) for a uniformly random permutation π of {1, 2, . . . , n}, leading to the following results: • Consider the problem of finding a point in {1, 2, . . . , n} with the minimum sum of distances to all points. We show that this problem has a randomized algorithm that (1) alwa...