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On Approximation by Stancu Type Bernstein–Schurer Polynomials in Compact Disks

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Abstract

In the present paper, we introduce Stancu type Bernstein–Schurer polynomials and their Kantorovich variants. The exact order of simultaneous approximation and Voronovaskaja-type results with quantitative estimate for analytic functions in compact disks are obtained. Our results improve those of Anastassiou and Gal (Comput Math Appl 58:734–743, 2009).

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References

  1. Anastassiou, G.A., Gal, S.G.: Approximation by complex Bernstein–Schurer and Kantorovich–Schurer polynomials in compact disks. Comput. Math. Appl. 58, 734–743 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Lorentz, G.G.: Bernstein Polynomials, 2nd edn. Chelsea Publishers, New York (1986)

    MATH  Google Scholar 

  3. Gal, S.G.: Shape Preserving Approximation by Real and Complex Polynomials. Birkhäuser Publishers, Boston (2008)

    Book  MATH  Google Scholar 

  4. Gal, S.G.: Approximation by complex genuine Durrmeyer type polynomials in compact disks. Appl. Math. Comput. 217, 1913–1920 (2010)

    MATH  MathSciNet  Google Scholar 

  5. Gal, S.G.: Approximation by complex Bernstein–Stancu polynomials in compact diskes. Result Math. 53, 245–256 (2009)

    Article  MATH  Google Scholar 

  6. Gal, S.G., Gupta, V.: Quantitative estimates for a new complex Durrmeyer operator in compact disks. Appl. Math. Comput. 218, 2944–2951 (2011)

    MATH  MathSciNet  Google Scholar 

  7. Gupta, V.: Approximation properties by Bernstein–Durrmeyer type operators. Complex Anal. Op. Theory 7, 363–374 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gupta, V., Agarwal, R.P.: Convergence Estimates in Approximation Theory. Springer, Switzerland (2014)

    Book  MATH  Google Scholar 

  9. Mahmudov, N.I.: Approximation by \(q\)-Durrmeyer type polynomials in compact disks in the case \(q>1\). Appl. Math. Comput. 237, 293–303 (2014)

    MATH  MathSciNet  Google Scholar 

  10. Mahmudov, N.I., Kara, M.: Approximation properties of weighted Kantorovich type operators in compact disks. J. Inequal. Appl. 2015, 46 (2015). doi:10.1186/s13660-015-0571-1

    Article  MATH  MathSciNet  Google Scholar 

  11. Mahmudov, N.I., Gupta, V.: Approximation by genuine Durrmeyer–Stancu polynomials in compact diskes. Math. Comput. Model. 55, 278–285 (2012)

    Article  MATH  Google Scholar 

  12. Stancu, D.D.: On a generalization of Bernstein polynomials. Stud. Univ. Babes-Bolyai Ser. Math. 14, 31–44 (1969)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, Zhejiang, China

    Bing Jiang & Dansheng Yu

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  1. Bing Jiang
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  2. Dansheng Yu
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Correspondence to Dansheng Yu.

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Jiang, B., Yu, D. On Approximation by Stancu Type Bernstein–Schurer Polynomials in Compact Disks. Results Math 72, 1623–1638 (2017). https://doi.org/10.1007/s00025-017-0740-2

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  • DOI: https://doi.org/10.1007/s00025-017-0740-2

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