A note on the Choquet type operators
Abstract
In this note the Choquet type operators are introduced, in connection to 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 H\"older's inequality within the framework of monotone and sublinear operators acting on spaces of continuous functions.
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