Results in Mathematics

, 74:28 | Cite as

Approximation by Durrmeyer Type Bernstein–Stancu Polynomials in Movable Compact Disks

  • Bing Jiang
  • Dansheng YuEmail author


In the present paper, we introduce a kind of complex Durrmeyer type Bernstein–Stancu polynomials in movable disks. Approximation properties by the new polynomials for analytic functions in the movable compact disks are considered.


Complex Durrmeyer type Bernstein–Stancu polynomials movable compact disks approximation rates 

Mathematics Subject Classification

30E10 41A25 



  1. 1.
    Anastassious, G.A., Gal, S.G.: Approximation by complex Bernstein–Durrmeyer polynomials in compact disks. Mediter. J. Math. 7, 471–482 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dong, L.X., Yu, D.S.: Pointwise approximation by a Durrmeyer variant of Bernstein–Stancu operators. J. Inequal. Appl. 2017(2017), 28 (2017). MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gal, S.G.: Shape Preserving Approximation by Real and Complex Polynomials. Birkhäuser Publ., Basel (2008)CrossRefGoogle Scholar
  4. 4.
    Gadjiev, A.D., Ghorbanalizaeh, A.M.: Approximation properties of new type Bernstein–Stancu polynomials of one and two variables. Appl. Math. Comput. 216, 890–901 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Gal, S.G.: Approximation by complex Bernstein–Stancu polynomials in compact disks. Results Math. 53, 245–256 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gal, S.G.: Approximation by complex Bernstein–Kantorovich and Kantorovich–Stancu polynomials and their iterates in compact disks. Rev. Anal. Numer. Theor. Approx. 37, 159–168 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Gal, S.G.: Exact orders in simultaneous approximation by complex Bernstein–Stancu polynomials. Revue Anal. Numer. Theor. Approx. 37, 47–52 (2008)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Içöz, G.: A Kantorovich variant of a new type Bernstein–Stancu polynomials. Appl. Math. Comput. 218, 8552–8560 (2012)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Jiang, B., Yu, D.S.: On approximation by Bernstein–Stancu polynomials in movable compact disks. Results Math. 3, 1623–1638 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Jiang, B., Yu, D.S.: On approximation by Stancu type Bernstein–Schurer polynomials in compact disks. Results Math. 3, 1–9 (2017)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Lorentz, G.G.: Bernstein Polynomials, 2nd edn. Chelsea Publ, New York (1986)zbMATHGoogle Scholar
  12. 12.
    Mahmudov, N.I., Gupta, V.: Approximation by genuine Durrmeyer–Stancu polynomials in compact disks. Math. Comput. Model. 55(3), 278–285 (2013)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Ren, M.Y., Zeng, X.M., Zeng, L.: Approximation by complex Durrmeyer–Stancu type operators in compact disks. J. Inequl. Appl. 2013, 442 (2013). CrossRefzbMATHGoogle Scholar
  14. 14.
    Stancu, D.D.: Approximation of functions by a new class of linear polynomials operators. Rev. Roum. Math. Pures Appl. 13, 1173–1194 (1968)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Stancu, D.D.: On a generalization of Bernstein polynomials. Stud. Univ. “Babes-Bolyai” Ser. Math. 14, 31–44 (1969)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Taşdelen, F., Başcanbaz-Tunca, G., Erençin, A.: On a new type Bernstein–Stancu operators. Fasc. Math. 48, 119–128 (2012)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Wang, M.L., Yu, D.S., Zhou, P.: On approximation by Bernstein–Stancu type operators. Appl. Math. Comput. 246, 79–87 (2014)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHangzhou Normal UniversityHangzhouChina

Personalised recommendations