Generalized Bernstein operators defined by increasing nodes

J. M. Aldaz; H. Render

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arXiv · 1803.05343

Generalized Bernstein operators defined by increasing nodes

J. M. Aldaz·H. Render

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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-{\guillemotleft}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 $[a,b]$.

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BibTeX RIS

J. M. Aldaz, H. Render. 2018-03-14. Generalized Bernstein operators defined by increasing nodes. https://arxiv.org/abs/1803.05343

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