Year: 2018
Type: preprint
Abstract: We study certain generalizations of the classical Bernstein operators, defined via increasing sequences of nodes. Such operators are required to fix two functions, $f_0$ and $f_1$, such that $f_0 > 0$ and $f_1/ f_0$ is increasing on an interval $[a,b]$. A characterization regarding when this can be done is presented. From it we obtain, under rather general circumstances, the following necessary condition for existence: if nodes are non-«decreasing, then $(f_1/f_0)^\prime >0 $ on $(a,b)$, while if nodes are strictly increasing, then $(f_1/f_0)^\prime >0 $ on $[a,b]$.
Source: arXiv (Cornell University)
Authors: Aldaz, J. M., Render, H.
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2789620886