Related papers: Approximations of Set-Valued Functions by Metric L…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…
In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable…
In approximation theory classical discrete operators, like generalized sampling, Sz\'{a}sz-Mirak'jan, Baskakov and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of…
We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…
In this work we construct subdivision schemes refining general subsets of R^n and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed…
In Mergelyan type approximation we uniformly approximate functions on compact sets K by polynomials or rational functions or holomorphic functions on varying open sets containing K. In the present paper we consider analogous approximation,…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to non-empty compact subsets of $\mathbb{R}^d$, $F: [a,b] \to K(\mathbb{R}^d)$, we discuss the problem of computing good approximations of F. We…
In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the…
We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
We design quasi-interpolation operators based on piecewise polynomial weight functions of degree less than or equal to $p$ that map into the space of continuous piecewise polynomials of degree less than or equal to $p+1$. We show that the…