# Bezier variant of the Bernstein–Durrmeyer type operators

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2017-01-02

AUTHORS ABSTRACT

In the present paper, we introduce the Bezier-variant of Durrmeyer modification of the Bernstein operators based on a function τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}, which is infinite times continuously differentiable and strictly increasing function on [0, 1] such that τ(0)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (0)=0$$\end{document} and τ(1)=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (1)=1$$\end{document}. We give the rate of approximation of these operators in terms of usual modulus of continuity and K-functional. Next, we establish the quantitative Voronovskaja type theorem. In the last section we obtain the rate of convergence for functions having derivative of bounded variation. More... »

PAGES

1341-1358

### References to SciGraph publications

• 2015-05-08. The new forms of Voronovskaya’s theorem in weighted spaces in POSITIVITY
• 2003-05. Positive linear operators which preserve x2 in ACTA MATHEMATICA HUNGARICA
• 2009-06-29. General King-Type Operators in RESULTS IN MATHEMATICS
• 2009-05-05. A New Estimate on the Rate of Convergence of Durrmeyer-Bézier Operators in JOURNAL OF INEQUALITIES AND APPLICATIONS
• 1987. Moduli of Smoothness in NONE
• ### Journal

TITLE

Results in Mathematics

ISSUE

3

VOLUME

72

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00025-016-0639-3

DOI

http://dx.doi.org/10.1007/s00025-016-0639-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009224441

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