@misc{10481/92536,
year = {2014},
month = {6},
url = {https://hdl.handle.net/10481/92536},
abstract = {A general frame for Bernstein-type operators that preserve derivatives is given. We introduce
Bernstein-type operators based in the weighted classical Jacobi inner product on the interval
[0, 1] that extend the well known Bernstein–Durrmeyer operator as well as some other types
of Bernstein operators that appear in the literature. Apart from standard results, we deduce
properties about the preservation of derivatives and prove that classical Jacobi orthogonal
polynomials on [0, 1] are the eigenfunctions of these operators. We also study the limit cases
when one of the parameters of the Jacobi polynomials is a negative integer. Finally, we study
several numerical examples.},
publisher = {SpringerLink},
title = {Bernstein–Jacobi-type operators preserving derivatives},
doi = {https://doi.org/10.1007/s40314-024-02796-2},
author = {Lara Velasco, David and Pérez Fernández, Teresa Encarnación},
}