A note on the Choquet type operators
arXiv:2004.07073 · doi:10.1007/s00010-021-00803-z
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 Hölder's inequality within the framework of monotone and sublinear operators acting on spaces of continuous functions.
13 pages