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On a new type Bernstein-Stancu operators

Taşdelen, Başcanbaz-Tunca G., Erençin

Fasciculi Mathematici

2012

Nr 48

119--128

In the present paper, firstly we obtain a functional differential equation corresponding to new type Bernstein-Stancu operators defined in [8]. Next we introduce some properties of these new type operators. In the end k-th order generalization of such operators is established.

Some properties of multivariate beta operator

Başcanbaz-Tunca G., Tuncer Y.

Fasciculi Mathematici

2009

Nr 41

31-43

This work relates to multivariate beta operator which is expressed shortly as Bn. We show that the operator preserves Lipschitz constant of a Lipschitz continuous function and semi-additivity of the relevant operand. Furthermore, we provide an r-th order generalisation, Bn (r), of Bn.