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Approximation by Bivariate Bernstein-Durrmeyer Operators on a Triangle |
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PP: 693-702 |
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doi:10.18576/amis/110308
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Author(s) |
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Meenu Goyal,
Arun Kajla,
P. N. Agrawal,
Serkan Araci,
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Abstract |
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| 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. |
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