A Weighted Generalization of the Classical Kantorovich Operator. II: Saturation

In [1], we have introduced a new weighted type of modification of the classical Kantorovich operator. The advantage of this operator is that there is no restriction on the parameters of the weight, and the class of functions is wider than in the earlier version of the weighted operator (cf. the monograph of Ditzian and Totik [3]). Direct and converse theorems and a Voronovskaya-type relation were proved. Here we solve the saturation problem of the operator (Theorem 2. 1). We follow the method developed in [3], but the details are much more involved. A surprising fact emerges in determining the trivial class of saturation (Theorem 3. 1). © 2012 Springer Basel AG.