Abstract
In the present paper, we obtain some approximation properties for the bivariate Bernstein-Durrmeyer operators on a triangle. We characterize the rate of convergence in terms of K−functional and the usual and second order modulus of continuity. We estimate the order of approximation by Voronovskaja type result and illustrate the convergence of these operators to a certain function through graphics using Mathematica algorithm. We also discuss the comparison of the convergence of the bivariate Bernstein-Durrmeyer operators and the bivariate Bernstein-Kantorovich operators to the function through illustrations using Mathematica. Lastly, we study the simultaneous approximation for first order partial derivatives and the shape preserving properties of these operators.
Suggested Reviewers
N/A
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/amis/110308
Recommended Citation
Goyal, Meenu; Kajla, Arun; N. Agrawal, P.; and Araci, Serkan
(2017)
"Approximation by Bivariate Bernstein-Durrmeyer Operators on a Triangle,"
Applied Mathematics & Information Sciences: Vol. 11
:
Iss.
3
, Article 8.
DOI: http://dx.doi.org/10.18576/amis/110308
Available at:
https://dc.naturalspublishing.com/amis/vol11/iss3/8