Skip to main content
SpringerLink
Log in

Quantitative Estimates for Differences of Baskakov-Type Operators

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

In the present paper, we establish the quantitative estimates in terms of weighted modulus of continuity, for the differences of Baskakov operators with Baskakov–Szász operators, Baskakov–Kantorovich operators and Genuine Baskakov–Durrmeyer type operators. Also, we find the estimates for the mutual differences of these operators. Finally, we provide an estimate for the difference of operators by direct method.

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. Acar, T., Aral, A., Raşa, I.: The new forms of Voronovskaja’s theorem in weighted spaces. Positivity 20, 25–40 (2016)

    Article  MathSciNet  Google Scholar 

  2. Acu, A.M., Raşa, I.: New estimates for differences of positive linear operators. Numer. Algorithms 73, 775–789 (2016)

    Article  MathSciNet  Google Scholar 

  3. Aral, A., Inoan D., and Raşa, I.: On differences of linear positive operators. Anal. Math. Phys. https://doi.org/10.1007/s13324-018-0227-7

    Article  MathSciNet  Google Scholar 

  4. Finta, Z.: On converse approximation theorems. J. Math. Anal. Appl. 312, 159–180 (2005)

    Article  MathSciNet  Google Scholar 

  5. Gonska, H., Pitul, P., Raşa, I.: On differences of positive linear operators. Carpathian J. Math. 22(1–2), 65–78 (2006)

    MathSciNet  MATH  Google Scholar 

  6. Gonska, H., Raşa, I.: Differences of positive linear operators and the second order modulus. Carpathian J. Math. 24(3), 332–340 (2008)

    MATH  Google Scholar 

  7. Gupta, V.: A note on modified Baskakov type operators. Approx. Theory Appl. 10(3), 74–78 (1994)

    MathSciNet  MATH  Google Scholar 

  8. Gupta, V.: Differences of operators of Lupaş type. Constr. Math. Anal. 1(1), 9–14 (2018)

    Google Scholar 

  9. Gupta, V.: General estimates for the difference of operators. Comput. Math. Methods 1(2), e1018 (2019). https://doi.org/10.1002/cmm4.1018

    Article  Google Scholar 

  10. Gupta, V.: On difference of operators with applications to Szász type operators. RACSAM 113, 2059–2071 (2018). https://doi.org/10.1007/s13398-018-0605-x

    Article  MATH  Google Scholar 

  11. Gupta, V., Rassias, T.M., Agrawal, P.N., Acu, A.M.: Recent Advances in Constructive Approximation Theory. Springer, Cham (2018)

    Book  Google Scholar 

  12. Gupta, V., Srivastava, G.S.: Simultaneous approximation by Baskakov-Szász type operators. Bull. Math. Soc. Sci. Math. Roum. 37(85), 73–85 (1993)

    MATH  Google Scholar 

  13. Zhang, C., Zhu, Z.: Preservation properties of Baskakov-Kantorovich operators. Comput. Math. Appl. 57, 1450–1455 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Netaji Subhas University of Technology (Formerly Netaji Subhas Institute of Technology), Sector 3 Dwarka, New Delhi, 110078, India

    Vijay Gupta & Deepika Agrawal

  2. Institute of Mathematics, University of Zurich, 8057, Zurich, Switzerland

    Michael Th. Rassias

  3. Moscow Institute of Physics and Technology, Institutskiy Per, d. 9, Dolgoprudny, Russia, 141700

    Michael Th. Rassias

  4. Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ, 08540, USA

    Michael Th. Rassias

Authors
  1. Vijay Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Deepika Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Th. Rassias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Th. Rassias.

Additional information

Communicated by Ronen Peretz.

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

Gupta, V., Agrawal, D. & Rassias, M.T. Quantitative Estimates for Differences of Baskakov-Type Operators. Complex Anal. Oper. Theory 13, 4045–4064 (2019). https://doi.org/10.1007/s11785-019-00950-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11785-019-00950-x

Keywords

Search

Navigation