Related papers: Uniform Approximation of Continuous Functions by N…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
We answer the question: "on which metric spaces $(M,d)$ are all continuous functions uniformly continuous?" Our characterization theorem improves and generalizes a previous result due to Levine and Saunders, and in particular is applicable…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Let the metric space $\mathbb R^n \setminus \sim$ be the metric space of $n$-sized unordered tuples of real numbers. In the following, it will be shown that if a function $\varphi: \mathbb R^m \to \mathbb R^n \setminus \sim$ is continuous,…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing…
In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…
We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise…
We obtain an interesting inequalities for uniformly continuous functions in the normed spaces: $\|f(x)\|\leq a\|x\|+b$ for some $a,b> 0$.
In this survey, we use (more or less) elementary means to establish the well-known result that for any given smooth multivariate function, the respective multivariate Bernstein polynomials converge to that function in all derivatives on…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…
Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…