Abstract
In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for a new type of complex Durrmeyer polynomials, attached to analytic functions in compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for this kind of Durrmeyer polynomials, namely the extensions of approximation properties with exact quantitative estimates, from the real interval [0, 1] to compact disks in the complex plane.
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References
Anastassiou G.A., Gal S.G.: Approximation by complex Bernstein–Durrmeyer polynomials in compact disks. Mediterr. J. Math. 7(4), 471–482 (2010)
Gal S.G.: Approximation by complex Bernstein and convolution-type operators. World Scientific Publ. Co, Singapore (2009)
Gal S.G.: Approximation by complex genuine Durrmeyer type polynomials in compact disks. Appl. Math. Comput. 217, 1913–1920 (2010)
Gupta V., Maheshwari P.: Bezier variant of a new Durrmeyer type operators. Rev. Mat. Univ. Parma. 7(2), 9–21 (2003)
Lorentz G.G.: Bernstein polynomials. 2nd edn. Chelsea Publ, New York (1986)
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Gal, S.G., Gupta, V. Approximation by a Durrmeyer-type operator in compact disks. Ann Univ Ferrara 57, 261–274 (2011). https://doi.org/10.1007/s11565-011-0124-6
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DOI: https://doi.org/10.1007/s11565-011-0124-6
Keywords
- Complex Durrmeyer-type operators
- Complex simultaneous approximation
- Voronovskaja-type result
- Exact degrees of approximation