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arXiv · 1803.01673

Generalized Bernstein operators on the classical polynomial spaces

J. M. Aldaz·H. Render
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Abstract

We study generalizations of the classical Bernstein operators on polynomial spaces, where instead of fixing $\mathbf{1}$ and $x$, we require that $\mathbf{1}$ and a strictly increasing polynomial $f_1$ be fixed. Via several examples, we exhibit the diversity of behaviours in this more general setting. We also prove that for sufficiently large dimensions, there always exist generalized Bernstein operators fixing $\mathbf{1}$ and $f_1$, and converging to the identity.

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J. M. Aldaz, H. Render. 2018-03-05. Generalized Bernstein operators on the classical polynomial spaces. https://arxiv.org/abs/1803.01673

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