Approximation by Bivariate Bernstein-Durrmeyer Operators on a Triangle

Authors

Meenu Goyal, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, IndiaFollow
Arun Kajla, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, IndiaFollow
P. N. Agrawal, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, IndiaFollow
Serkan Araci, Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyFollow

Author Country (or Countries)

India

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.

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://digitalcommons.aaru.edu.jo/amis/vol11/iss3/8