The first absolute moment for some operators

In this paper we will determinate the first absolute moments for Bernstein, Szász-Mirakjan, Bleimann-Butzer-Hahn, Meyer-König and Zeller operators. For the Szász-Mirakjan operators we give some properties with the absolute moment of high order

Some general Kantorovich type operators

A general class of linear and positive operators of Kantorovich-type is constructed. The operators of this type which preserve exactly two test functions from the set $\{e_0, e_1, e_2\}$ are determined and their approximation properties and convergence theorems are studied

The generalization of some results for Bernstein and Stancu operators

In the present paper we generalize some results for Bernstein and Stancu operators. Firstly, we establish a relationship between two results concerning calculation of test functions by Bernstein operators. Secondly, using this relationship and some known results we prove in every case a Voronovskaja type theorem, the uniform convergence and the order of approximation for Bernstein and Stancu operators.</jats:p

Schurer operators of King type

A class of linear and positive operators defined by finite sum which generalizes the classical Schurer’s operators in the King sense is constructed. For the mentioned class of operators, uniform convergences results, error estimations in terms of modulus of continuity and Voronovskaja type theorems are established.</jats:p

Note on a Schurer-Stancu-type operator

The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions e0 and e1 are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.</jats:p