Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube
Classical Analysis and ODEs
2024-05-28 v1 Functional Analysis
Abstract
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its square. In particular, we prove uniform convergence, by means of two different approaches, as well as a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function.
Cite
@article{arxiv.2405.16935,
title = {Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube},
author = {Laura Angeloni and Danilo Costarelli and Chiara Darielli},
journal= {arXiv preprint arXiv:2405.16935},
year = {2024}
}