Abstract
In this paper, the exact order of approximation and Voronovskaja type theorems with quantitative estimate for complex genuine Pólya-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. Our results show that extension of the complex genuine Pólya-Durrmeyer polynomials from real intervals to compact disks in the complex plane extends approximation properties (with quantitative estimates).
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The authors are thankful to the referee(s) for valuable suggestions, leading to overall improvements in the paper.
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Communicated by Raymond Mortini.
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Gupta, V., Malik, N. Approximation of functions by complex genuine Pólya-Durrmeyer operators. Comput. Methods Funct. Theory 17, 3–17 (2017). https://doi.org/10.1007/s40315-016-0167-x
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DOI: https://doi.org/10.1007/s40315-016-0167-x
Keywords
- Complex genuine Pólya-Durrmeyer operators
- Voronovskaja’s theorem
- Binet’s formula
- Approximation in compact disks