Related papers: Direct and inverse theorems for Bernstein operator…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…
We prove that several forms of the Bernstein polynomials with integer coefficients possess the property of simultaneous approximation, that is, they approximate not only the function but also its derivatives. We establish direct estimates…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…
We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…
Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn…
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…
We extend two theorems of Krein concerning entire functions of Cartwright class, and give applications for the Bernstein weighted approximation problem.
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and…
We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
The aim of this paper is to study variation detracting property and con- vergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are…
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.
We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our…
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…
Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i=0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is…
We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse…