On the rates of pointwise convergence for Bernstein polynomials

Autor:	Adell, José A., Cárdenas-Morales, Daniel, López-Moreno, Antonio J.
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs 41A10 41A25 41A36 60E05
Druh dokumentu:	Working Paper
Popis:	Let $f$ be a real function defined on the interval $[0,1]$ which is constant on $(a,b)\subset [0,1]$, and let $B_nf$ be its associated $n$th Bernstein polynomial. We prove that, for any $x\in (a,b)$, $|B_nf(x)-f(x)|$ converges to $0$ as $n\rightarrow \infty $ at an exponential rate of decay. Moreover, we show that this property is no longer true at the boundary of $(a,b)$. Finally, an extension to Bernstein-Kantorovich type operators is also provided Comment: 7 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.10135 Zobrazit plný text záznamu View this record from Arxiv