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arXiv · 2308.13216

A generalization of a theorem of Brass and Schmeisser

Tomasz Szostok
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Abstract

Let $n$ be an odd positive integer. It was proved by Brass and Schmeisser that for every quadrature $$\mathcal{Q}=\alpha_1f(x_1)+\dots+\alpha_mf(x_m),$$ (with positive weights) of order at least $n+1$ and for every $n-$convex function $f,$ the value of $Q$ on $f$ lies between the values of Gauss and Lobatto quadratures of order $n+1$ calculated for the same function $f$. We generalize this result in two directions, replacing $Q$ by an integral with respect to a given measure and allowing the number $n$ to any positive integer (for even $n$ Radau quadratures replace Gauss and Lobatto ones

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Tomasz Szostok. 2023-08-25. A generalization of a theorem of Brass and Schmeisser. https://arxiv.org/abs/2308.13216

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