Local smoothness of functions and Bernstein-Durrmeyer operators

Pointwise approximation for a type of Bernstein-Durrmeyer operators

*Correspondence: [email protected] College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People’s Republic of China Abstract We give the direct and inverse approximation theorems for a new type of Bernstein-Durrmeyer operators with the mod...

Pointwise approximation by a Durrmeyer variant of Bernstein-Stancu 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.

Blending Type Approximation by Bernstein-durrmeyer Type Operators

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absol...

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights

Quantitative estimates in approximation by Bernstein-Durrmeyer-Choquet operators with respect to monotone and submodular set functions

For the qualitative results of pointwise and uniform approximation obtained in [10], we present general quantitative estimates in terms of the modulus of continuity and in terms of a K-functional, for the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x , written in terms of the Choquet integral with respect to a family of monotone and submodular set functions, Γn,x, on the standar...