Durrmeyer Modification of Lupaş Type Baskakov Operators Based on IPED

  • Minakshi DhamijaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 306)


The purpose of this paper is to consider Durrmeyer variant of Lupaş type Baskakov operators having inverse Pólya–Eggenberger distribution basis function. We derive some direct results which include uniform convergence, pointwise approximation via modulus of continuity and asymptotic formula.


Stancu operators Baskakov operators Durrmeyer operators Inverse Pólya–Eggenberger distribution 

2010 Mathematics Subject Classication

41A25 41A36 


  1. 1.
    A.M. Acu, C.V. Muraru, D.F. Sofonea, V.A. Radu, Some approximation properties of a Durrmeyer variant of q-Bernstein-Schurer operators. Math. Methods Appl. Sci. 39(18), 5636–5650 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    F. Altomare, M. Campiti, Korovkin-Type Approximation Theory and its Application, de Gruyter Studies in Mathematics, vol. 17 (Walter de Gruyter & Co., Berlin, 1994)Google Scholar
  3. 3.
    V.A. Baskakov, A sequence of linear positive operators in the space of continuous functions. Dokl. Acad. Nauk. SSSR 113, 249–251 (1957)MathSciNetzbMATHGoogle Scholar
  4. 4.
    S.N. Bernstein, Démonstration du théoréme de Weierstrass fondée sur le calcul de probabilités. Commun. Sco. Math. Charkov 13(2), 1–2 (1912)zbMATHGoogle Scholar
  5. 5.
    N. Deo, M. Dhamija, Generalized positive linear operators based on PED and IPED. Iran. J. Sci. Technol. Trans. Sci. 43 (2018), Scholar
  6. 6.
    N. Deo, M. Dhamija, D. Miclăuş, Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution. Appl. Math. Comput. 273, 281–289 (2015)Google Scholar
  7. 7.
    N. Deo, M. Dhamija, Jain–Durrmeyer operators associated with the inverse Pólya-Eggenberger distribution. Appl. Math. Comput. 286, 15–22 (2016)MathSciNetzbMATHGoogle Scholar
  8. 8.
    R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)CrossRefGoogle Scholar
  9. 9.
    M. Dhamija, N. Deo, D. Miclăuş, Modified Baskakov operators based on inverse Pólya-Eggenberger Distribution. (Communicated)Google Scholar
  10. 10.
    F. Eggenberger, G. Pólya, Über die statistik verkerter vorgänge. Z. Angew. Math. Mech. 1, 279–289 (1923)CrossRefGoogle Scholar
  11. 11.
    Z. Finta, On approximation properties of Stancu’soperators. Stud. Univ. Bolyai Math. XLVII(4), 47–55 (2002)Google Scholar
  12. 12.
    V. Gupta, R.P. Agarwal, Convergence Estimates in Approximation Theory (Springer, New York, 2014)Google Scholar
  13. 13.
    V. Gupta, T.M. Rassias, Lupaş-Durrmeyer operators based on Polya distribution. Banach J. Math. Anal. 8(2), 145–155 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    H.S. Jung, N. Deo, M. Dhamija, Pointwise approximation by Bernstein type operators in mobile interval. Appl. Math. Comput. 214(1), 683–694 (2014)MathSciNetzbMATHGoogle Scholar
  15. 15.
    P.P. Korovkin, Convergence of linear positive operators in the spaces of continuous functions(Russian). Doklady Akad. Nauk. SSSR(N.N.) 90, 961–964 (1953)Google Scholar
  16. 16.
    L. Lupaş, A. Lupaş, Polynomials of binomial type and approximation operators, Stud. Univ. Babeş-Bolyai Math. 32(4), 61–69 (1987)Google Scholar
  17. 17.
    D.D. Stancu, Approximation of functions by a new class of linear polynomial operators. Rev. Roum. Math. Pures Appl. 13, 1173–1194 (1968)MathSciNetzbMATHGoogle Scholar
  18. 18.
    D.D. Stancu, Two classes of positive linear operators. Anal. Univ. Timişoara Ser. Mat. 8, 213–220 (1970)Google Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsShaheed Rajguru College of Applied Sciences for WomenNew DelhiIndia

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