A note on the Choquet type operators (Q2029453)

In a recent work of the authors [Mediterr. J. Math. 17, No. 5, Paper No. 145, 14 p. (2020; Zbl 07246867)], a nonlinear extension of the well-known Korovkin theorem was obtained. A quantative estimate concerning this extension theorem in the case of Bernstein-Kantorovich-Choquet operators is proved. The proof essentially uses a generalization of the Cauchy-Bunyakovsky-Schwarz inequality for Choquet type operators. It is noted that a similar proof works also for the Szaśz-Mirakjan-Kantorovich-Choquet and for Baskakov-Kantorovich-Choquet operators.