一类广义Bernstein-Kantorovich算子的逼近性质

Approximation properties of a class of generalized Bernstein-Kantorovich operators

引入一类新的基于参数α的Bernstein-Kantorovich算子,研究算子的保形性质,即保单调性和保凸性,同时给出该算子Voronovskaja型的逼近定理.

A kind of new Bernstein-Kantorovich operators based on parameterαare introduced.Some shape preserving properties of these operators,namely,monotonicity and convexity preservation are studied.At the same time,the approximation theorems for the Voronovskaja type operators are presented.