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arXiv · 1609.00973

Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation

Klaudiusz Czudek
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Abstract

We prove the $\Lambda$-variation diminishing property of the Bernstein and Kantorovich polynomials. Next we apply this result to characterize the space $C\Lambda BV_c$ as the closure of the space of polynomials in the $\Lambda BV$ norm. A new proof of the separability of $C\Lambda BV_c$ is given.

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Klaudiusz Czudek. 2016-09-04. Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation. https://arxiv.org/abs/1609.00973

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