Skip to main content
SpringerLink
Log in

Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

We investigate the weighted approximation of functions in \(L_p\)-norm by Kantorovich modifications of the classical Szász–Mirakjan operator, with weights of type \((1+x)^{\alpha }\), \(\alpha \in \mathbb {R}\). By defining an appropriate K-functional we prove direct inequality for them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berens, H., Xu, Y.: On Bernstein–Durrmeyer Polynomials with Jacobi–Weights, Approximation Theory and Functional Analysis. Academic Press, New York (1990)

    Google Scholar 

  2. Ditzian, Z., Ivanov, K.G.: Strong converse inequalities. J. Anal. Math. 61, 61–111 (1993)

    Article  MathSciNet  Google Scholar 

  3. Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer, Berlin (1987)

    Book  Google Scholar 

  4. Draganov, B.R., Ivanov, K.G.: A new characterization of weighted Peetre K-functionals. Constr. Approx. 21, 113–148 (2005)

    MathSciNet  MATH  Google Scholar 

  5. Draganov, B.R., Ivanov, K.G.: A new characterization of weighted Peetre K-functionals (II). Serdica Math. J. 33, 59–124 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Draganov, B.R., Ivanov, K.G.: Natural weights for uniform approximation by the Szász–Mirakjan operator. Constr. Theory Funct. Sozopol 2013, 1–27 (2014)

    MATH  Google Scholar 

  7. Draganov, B.R., Ivanov, K.G.: A new characterization of weighted Peetre K-functionals (III). Constr. Theory Funct. Sozopol 2016, 75–97 (2018)

    MATH  Google Scholar 

  8. Draganov, B.R., Gadjev, I.: Approximation of functions by the Szasz–Mirakjan–Kantorovich operator. Numer. Funct. Anal. Optim. 40, 7 (2019)

    Article  MathSciNet  Google Scholar 

  9. Mirakjan, G.M.: Approximation of continuous functions with the aid of polynomials... Dokl. Akad. Nauk SSSR 31, 201–205 (1941)

    Google Scholar 

  10. Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. Y. Res. Nat. Bur. Standards Sect. B 45, 239–245 (1950)

    Article  MathSciNet  Google Scholar 

  11. Totik, V.: Approximation by Szász–Mirakjan–Kantorovich Operators in \(L^p (p>1)\). Anal. Math. 9, 147–167 (1983)

    Article  MathSciNet  Google Scholar 

  12. Totik, V.: Uniform aproximation by Szász-Mirakjan-type operators. Acta Math. Hung. 41(3–4), 291–307 (1983)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Sofia, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria

    Ivan Gadjev & Parvan E. Parvanov

Authors
  1. Ivan Gadjev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Parvan E. Parvanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivan Gadjev.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gadjev, I., Parvanov, P.E. Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator. Results Math 76, 158 (2021). https://doi.org/10.1007/s00025-021-01472-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-021-01472-9

Keywords

Mathematics Subject Classification

Search

Navigation