We consider the Bézier variant of Chlodovsky–Durrmeyer operators Dn,α for functions f measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (Dn,αf) (x) at those x > 0 at which the one-sided limits f(x+), f(x−) exist. In the special case α = 1 the recent result of [14] concerning the Chlodovsky–Durrmeyer...

The paper contains the definition and certain approximation properties of a sequence Durrmeyer-type operators on simplex, which preserve affine functions make link between multidimensional "genuine" Durrmeyer Bernstein operators.

In the present paper, we introduce a kind of Durrmeyer variant of Bernstein-Stancu operators, and we obtain the direct and converse results of approximation by the operators.

This study introduces (p,q)-hybrid Durrmeyer-Stancu type linear positive operators, which are generalized forms of q-hybrid Durrmeyer-Stancu-type operators and examines their approximation properties. The first modulus continuity on a finite interval is introduced using Peetre’s K-functional. Then, the weighted theorem in space provided Gadzhiev’s Korovkin-type theorem. Finally, these operators...

We introduce a class of Bernstein-Durrmeyer operators with respect to an arbitrary measure on a multi-dimensional simplex. These operators generalize the well-known Bernstein-Durrmeyer operators with Jacobi weights. A motivation for this generalization comes from learning theory. In the talk, we discuss the question which properties of the measure are important for convergence of the operators....

In the present paper we introduce a q -analogue of the bivariate Durrmeyer operators. A convergence theorem for these operators is established and the rate of convergence in terms of modulus of continuity is determined. Also, a Voronovskaja type theorem has been investigated for these operators. Mathematics subject classification (2010): 41A10, 41A36.

and Applied Analysis 3 Since 1967, Durrmeyer introduced Bernstein-Durrmeyer operators, and there are many paperswhich studied theirproperties 1–7 . In 1991, Zhang studied the characterization of convergence forMn,1 f ;x with Jacobi weights. In 1992, Zhou 5 considered multivariate Bernstein-Durrmeyer operators Mn,d f ;x and obtained a characterization of convergence. In 2002, Xuan et al. studied...

In the present article, we propose the $(p,q)$ variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order.

in the present article, we propose the $(p,q)$variant of genuine baskakov durrmeyer operators. we obtain moments and establish some directresults, which include weighted approximation and results in terms of modulus of continuity of second order.

We study the rate of convergence in simultaneous approximation for the Bézier variant of Szász– Mirakyan–Durrmeyer operators by using the decomposition technique of functions of bounded variation. © 2006 Elsevier Inc. All rights reserved.