In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions...

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 this paper we introduce the Bézier variant of genuine-Durrmeyer type operators having Pólya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for funct...

This paper is a study of the degree of approximation by the linear combinations of the derivatives of certain Durrmeyer type integral modification of the Baskakov operators in terms of the higher order modulus of smoothness.

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....

Recommended by Vijay Gupta We obtain an estimate on the rate of convergence of Durrmeyer-Bézier operaters for functions of bounded variation by means of some probabilistic methods and inequality techniques. Our estimate improves the result of Zeng and Chen 2000. In 2000, Zeng and Chen 1 introduced the Durrmeyer-Bézier operators D n,α which are defined as follows: D n,α f, x n 1 n k0 Q α nk x 1 ...