arXiv subjects

Ana-Maria Acu

Publications and source records attributed to Ana-Maria Acu.

6 recordsLinked to original sources

arXiv2026

Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,\infty)$

We prove two Korovkin-type approximation theorems for sequences of positive linear operators acting on continuous functions on $[0,\infty)$. Under the assumption of pointwise convergence on suitable test functions, we establish pointwise convergence for all functions with polynomial or exponential growth. As direct applications, we obtain convergence results for the classical Baskakov and Sz\'asz--Mirakjan operators. The proposed method offers an elementary framework that can be applied to a broad class of positive linear operators.

math.NA↗

arXiv2024

Overiteration of $d$-variate tensor product Bernstein operators: a quantitative result

Extending an earlier estimate for the degree of approximation of overiterated univariate Bernstein operators towards the same operator of degree one, it is shown that an analogous result holds in the $d$-variate case. The method employed can be carried over to many other cases and is not restricted to Bernstein-type or similar methods.

math.CA↗

arXiv2023

An asymptotic formula for Aldaz-Kounchev-Render operators on the hypercube

We prove a version of a conjecture concerning the asymptotic behavior of the Aldaz-Kounchev-Render operators on the hypercube.

math.NA↗

arXiv2022

Poisson approximation to the binomial distribution: extensions to the convergence of positive operators

The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive linear operators. The proofs in these papers are given using probabilistic methods. We use similar methods, but in analytic terms. In this way we recover some known results and establish several new ones. In particular, we enlarge the list of the limit operators and give characterizations of them.

math.PR↗

arXiv2021

Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render

The Bernstein-type operator of Aldaz, Kounchev and Render (2009) is discussed. New direct results in terms of the classical second order modulus as well as in a modification following Marsden and Schoenberg are given.

math.CA↗

arXiv2015

Composite Bernstein Cubature

We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of the cubature formula are described in terms of moduli of continuity of order two. Also we include some results showing how non-multiplicative the integration functional is.

math.CA↗