Afrika Matematika

, Volume 29, Issue 1–2, pp 223–232 | Cite as

Charlier–Szász–Durrmeyer type positive linear operators

Article
  • 86 Downloads

Abstract

In the present paper, we study modified Szász–Durrmeyer positive linear operators involving Charlier polynomials, one of the discrete orthogonal polynomials which are generalization of Szász Durrmeyer operators. Also, King type modification of these operators is given. We obtain uniform convergence of our operators with the help of Korovkin theorem, asymptotic formula and the order of approximation by using classical modulus of continuity.

Keywords

Szász–Durrmeyer operators Charlier polynomials Modulus of continuity 

Mathematics Subject Classification

41A25 41A36 

Notes

Acknowledgements

The authors are extremely thankful to the referee for valuable comments and suggestions, leading to a better presentation of the paper.

References

  1. 1.
    Ciupa, A.: On the approximation by Favard–Szász type operators. Rev. Anal. Nuḿer. Théor. Approx. 25, 57–61 (1996)MathSciNetMATHGoogle Scholar
  2. 2.
    Deo, N., Bhardwaj, N., Singh, S.P.: Simultaneous approximation on generalized Bernstein–Durrmeyer operators. Afrika Mat. 24(1), 77–82 (2011)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Deo, N., Noor, M.A., Siddiqui, M.A.: On approximation by a class of new Bernstein type operators. Appl. Math. Comput. 201, 604–612 (2008)MathSciNetMATHGoogle Scholar
  4. 4.
    Gavrea, I., Rasa, I.: Remarks on some quantitative Korovkin-type results. Rev. Anal. Numer. Theor. Approx. 22(2), 173–176 (1993)MathSciNetMATHGoogle Scholar
  5. 5.
    Ismail, M.E.H.: Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge University Press, Cambridge (2005)CrossRefMATHGoogle Scholar
  6. 6.
    Jakimovski, A., Leviatan, D.: Generalized Szász operators for the approximation in the infinite interval. Mathematica (Cluj) 34, 97–103 (1969)MATHGoogle Scholar
  7. 7.
    King, J.P.: Positive linear operators which preserve \(x^2\). Acta Math. Hungar. 99, 203–208 (2003)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Mazhar, S.M., Totik, V.: Approximation by modifed Szász operators. Acta Sci. Math. (Szeged) 49(1–4), 257–269 (1985)MathSciNetMATHGoogle Scholar
  9. 9.
    Öksüzer, Ö., Karsli, H., Taşdelen, F.: Approximation by a Kantorovich variant of Szász operators based on Brenke-type polynomials. Mediterr. J. Math. 13(5), 3327–3340 (2016)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Sucu, S., Büyükyazici, I.: Integral operators containing Sheffer polynomials. BMATHAA 4(4), 56–66 (2012)MathSciNetMATHGoogle Scholar
  11. 11.
    Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Nat. Bur. Stand. 45, 239–245 (1950)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Taşdelen, F., Akta̧s, R., Altın, A.: A Kantorovich type of Szász operators including Brenke-type polynomials. Abstr. Appl. Anal. 2012, Article ID 867203, 13 pages (2012)Google Scholar
  13. 13.
    Varma, S.: On a generalization of Szász operators by multiple Appell polynomials. Stud. Univ. Babes Bolyai Math. 58, 361–369 (2013)MathSciNetMATHGoogle Scholar
  14. 14.
    Varma, S., Taşdelen, F.: On a generalization of Szász–Durrmeyer operators with some orthogonal polynomials. Stud. Univ. Babes Bolyai Math. 58(2), 225–232 (2013)MathSciNetMATHGoogle Scholar
  15. 15.
    Varma, S., Taşdelen, F.: Szász type operators involving Charlier polynomials. MCM 56, 118–122 (2012)CrossRefMATHGoogle Scholar
  16. 16.
    Varma, S., Sucu, S., İçöz, G.: Generalization of Szász operators involving Brenke type polynomials. CAMWA 64, 121–127 (2012)MATHGoogle Scholar
  17. 17.
    Zhuk, V.: Functions of Lip1 class and S. N. Bernstein’s polynomials. Vestnik Leningrad. univ. Mat. Mekh. Astron. 1, 25–30 (1989). (Russian)Google Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsDelhi Technological University (Formerly Delhi College of Engineering)DelhiIndia

Personalised recommendations