Shape preserving properties and monotonicity properties of the sequence of Choquet type integral operators. (English) Zbl 1463.41032
Summary: In this paper, for the univariate Bernstein-Kantorovich-Choquet, Szász-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet and Bernstein-Durrmeyer-Choquet operators written in terms of the Choquet integrals with respect to monotone and submodular set functions, we study the preservation of the monotonicity and convexity of the approximated functions and the monotonicity of some approximation sequences.
MSC:
| 41A29 | Approximation with constraints |
| 28A12 | Contents, measures, outer measures, capacities |
| 28A25 | Integration with respect to measures and other set functions |
| 41A35 | Approximation by operators (in particular, by integral operators) |
