Skip to main content
Log in

Durrmeyer variant of certain approximation operators

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In the present article, we introduce a Durrmeyer variant of certain approximation operators. We estimate the moment-generating function and moments of these operators employing the Lambert W function and establish some direct results. We further provide a composition of these operators with Szász–Mirakjan operators and estimate direct results for the composition operator. Additionally, we provide a graphical comparison of the approximation properties of the operators.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Data availibility

The authors confirm that there is no associated data.

References

  1. Abel, U., Gupta, V.: Construction of integral-type operators and discrete operators involving Laguerre polynomials, communicated

  2. Abel, U., Gupta, V.: Construction of new operators by composition of integral-type operators and discrete operators. Math. Pannon. (2024). https://doi.org/10.1556/314.2024.00001

    Article  Google Scholar 

  3. Acar, T., Aral, A., Gonska, H.: On Szász–Mirakyan operators preserving \(e^{2ax}, a>0\). Mediterr. J. Math. 14, 6 (2017). https://doi.org/10.1007/s00009-016-0804-7

    Article  Google Scholar 

  4. Acu, A.M., Gupta, V., Raşa, I., Sofonea, F.: Convergence of special sequences of semi-exponential operators. Mathematics 10(16), 2978 (2022). https://doi.org/10.3390/math10162978

    Article  Google Scholar 

  5. Acu, A.M., Heilmann, M., Raşa, I., Seserman, A.: Poisson approximation to the binomial distribution: extensions to the convergence of positive operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 117(4), Paper No. 162, 13 pp (2023). https://doi.org/10.1007/s13398-023-01497-5

  6. Boyanov, B.D., Veselinov, V.M.: A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. Roum. 14(62), 9–13 (1970)

    MathSciNet  Google Scholar 

  7. Govil, N.K., Gupta, V., Soybaş, D.: Certain new classes of Durrmeyer type operators. Appl. Math. Comput. 225, 195–203 (2013). https://doi.org/10.1016/j.amc.2013.09.030

    Article  MathSciNet  Google Scholar 

  8. Gupta, V., Acu, A.M., Sofonea, F.: Approximation of Baskakov type Pólya–Durrmeyer operators. Appl. Math. Comput. 294, 318–331 (2017). https://doi.org/10.1016/j.amc.2016.09.012

    Article  MathSciNet  Google Scholar 

  9. Gupta, V., Sharma, V.: On a composition of Ismail-May operator, communicated

  10. Holhoş, A.: The rate of approximation of functions in an infinite interval by positive linear operators. Stud. Univ. Babeş-Bolyai Math. 2, 133–142 (2010)

    MathSciNet  Google Scholar 

  11. Ismail, M., May, C.P.: On a family of approximation operators. J. Math. Anal. Appl. 63, 446–462 (1978)

    Article  MathSciNet  Google Scholar 

  12. Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Natl. Bureau Stand. 45(3), 239–245

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vijay Gupta.

Ethics declarations

Conflict of interest

The authors declare that they do not have any conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gupta, V., Sharma, V. Durrmeyer variant of certain approximation operators. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02113-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12190-024-02113-4

Keywords

Mathematics Subject Classification

Navigation