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...

A dilatation structure on a metric space, is a notion in between a group and a differential structure. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. There are two notions of linearity associated to dilatation structures: the linearity of a function between two dilata...

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of product, first show that each group is a torsion-free normed group. We give examples such and describe norms induced by products. Among other results, Hilbert groups, midconvex orthogonal subgroups are presented, Riesz representation theorem divisible proved.

The NEO Personality Inventory-Revised (NEO PI-R) measures normal personality characteristics and has demonstrated appropriate score reliability and validity. It is normed for two groups of individuals, college-age individuals 17 to 20 years old and adults 21 and older. Often, personality instruments normed on older individuals have been used with adolescent populations. To examine the appropria...

By using a random version of the theory of contractor introduced by Altman, we introduce and study a system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces. We construct some new iterative algorithms for solving this kind of nonlinear operator equations. We also prove some new existence theorems of solutions of a new system of nonli...

In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed spaces.

Let |·| be the standard Euclidean norm on ℝ n and let X=(ℝ ,∥·∥) a normed space. A subspace Y⊂X is strongly α-Euclidean if there constant t such that t|y|≤∥y∥≤αt|y| for every y∈Y, say it α-complemented ∥P Y ∥≤α, where P orthogonal projection from X to ∥ denotes operator of with respect X. We give an example space arbitrarily high dimension 2-Euclidean but contains no 2-dimensional both (1+ϵ)-Eu...

In previous work we established a multilinear duality and factorisation theory for norm inequalities pointwise weighted geometric means of positive linear operators defined on normed lattices. this paper extend the reach first time to setting general spaces. The scope includes Fourier restriction-type inequalities. We also sharpen our operators. Our results all share common theme: estimates mea...