Bernstein-Durrmeyer Operators Research Articles

A note on Bernstein type operators

In this note we give a counterexample to a result of Z. Ditzian and K. Ivanov. A direct theorm, on C[0,1] is also presented for Kantorovich operators and Bernstein-Durrmeyer operators.

A global inverse theorem on simultaneous approximation by Bernstein-Durrmeyer operators

We prove a global inverse result for simultaneous approximation by modified Bernstein operators as introduced by Durrmeyer in 1967. The main result of this note supplements and extends an earlier direct theorem of Heilmann and Müller and is given in terms of the so-called Ditzian-Totik modulus of second order.

On weighted approximation by Bernstein-Durrmeyer operators

In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.

Inverse theorems for some multidimensional operators

In this paper we introduce a new K-functional which is especially useful for non-Feller operators. Inverse theorems for multidimensional Bernstein-Sikkema and Bernstein-Durrmeyer operators are given on a simplex and on a cube.