Related papers: Statistical convergence in metric-like spaces
In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…
We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so-called "metric…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
We consider an one-dimensional inhomogeneous harmonic chain consisting of two different semi-infinite chains of harmonic oscillators. We study the Cauchy problem with random initial data. Under some restrictions on the interaction between…
We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and…
In this article, we study about the $\lambda$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_\lambda$-summable sequence and…
Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence…
In this paper we are going to discuss compactness in Lorentz sequence spaces. Firstly, it will be shown how to define such a space, check whether a sequence belongs to it and calculate its norm. Equipped with this knowledge, we will proceed…
Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
In the present paper, after recalling the Karcher mean in Hadamard spaces, we study the relation between convergence, almost convergence and mean convergence (respect to the defined mean) of a sequence in Hadamard spaces. These results…