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Approximation Properties by Bernstein–Durrmeyer Type Operators

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Abstract

In this paper, in order to make the convergence faster to a function being approximated, we modify the Bernstein–Durrmeyer type operators, which were introduced in Abel et al. (Nonlinear Anal Ser A Theory Methods Appl 68(11):3372–3381, 2008). The modified operators reproduce the constant and linear functions. The operators discussed here are different from the other modifications of Bernstein type operators. The Voronovskaja type asymptotic formula with quantitative estimate for a new type of complex Durrmeyer polynomials, attached to analytic functions in compact disks is obtained. Here, 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, 1/3] to compact disks in the complex plane.

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References

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Authors and Affiliations

  1. School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi, 110078, India

    Vijay Gupta

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  1. Vijay Gupta
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Correspondence to Vijay Gupta.

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Communicated by Guest Editors L. Littlejohn and J. Stochel.

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Gupta, V. Approximation Properties by Bernstein–Durrmeyer Type Operators. Complex Anal. Oper. Theory 7, 363–374 (2013). https://doi.org/10.1007/s11785-011-0167-9

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  • DOI: https://doi.org/10.1007/s11785-011-0167-9

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