In this note Choquet type operators are introduced in connection with Choquet’s theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear Korovkin type approximation theorem associated to Bernstein–Kantorovich–Choquet operators is proved. The paper also includes a large generalization of Hölder’s inequality within the framework of monotone and sublinear operators acting on spaces of continuous functions.

中文翻译：

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关于Choquet类型运算符的注释

在本说明中，结合了Choquet的可积性理论（不一定是加性集合函数），介绍了Choquet类型算子。根据它们的性质，证明了与Bernstein–Kantorovich–Choquet算子相关的非线性Korovkin型逼近定理的定量估计。本文还对作用在连续函数空间上的单调和亚线性算子框架内的Hölder不等式进行了广泛推广。