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.
Digital Object Identifier (DOI)
Goyal, Meenu; Kajla, Arun; N. Agrawal, P.; and Araci, Serkan
"Approximation by Bivariate Bernstein-Durrmeyer Operators on a Triangle,"
Applied Mathematics & Information Sciences: Vol. 11:
3, Article 8.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss3/8