Bernstein–Jacobi-type operators preserving derivatives Lara Velasco, David Pérez Fernández, Teresa Encarnación 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. 2024-06-12T10:32:40Z 2024-06-12T10:32:40Z 2014-06-12 info:eu-repo/semantics/article Comp. Appl. Math. 43, 277 (2024) https://hdl.handle.net/10481/92536 https://doi.org/10.1007/s40314-024-02796-2 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Attribution-NonCommercial-NoDerivatives 4.0 Internacional SpringerLink