Related papers: Generalized Metrics
We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…
Axiomatization of centrality measures often involves proving that something cannot hold by providing a counterexample (i.e., a graph for which that specific centrality index fails to have a given property). In the context of geometric…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supremum norm. We are interested in determining the generic…
The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) n-metric which assigns a value to a tuple of n points. We present two principles of constructing pseudo n-metrics. The first…
Comparative convexity is a generalization of convexity relying on abstract notions of means. We define the Jensen divergence and the Jensen diversity from the viewpoint of comparative convexity, and show how to obtain the generalized…
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
Biological processes like growth, aging, and disease progression are generally studied with follow-up scans taken at different time points, i.e., with image time series (TS) based analysis. Comparison between TS representing a biological…
Fr\'echet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider the behaviour of sample Fr\'echet means on normed spaces…
Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…
In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $\chi ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Mustafa and Sims [12] introduced the notion of $G$-metric as a possible generalization of usual notion of a metric space. The author generalized the notion of G-metric to more than three variables and introduced the concept of Generalized…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…