Skip to main content
SpringerLink
Log in

Approximation Properties of Chlodowsky Variant of (p, q) Szász–Mirakyan–Stancu Operators

  • Chapter
  • First Online:
Book cover Advances in Summability and Approximation Theory

  • 319 Accesses

Abstract

In the present paper, we introduce the Chlodowsky variant of (p, q) Szász–Mirakyan–Stancu operators on the unbounded domain which is a generalization of (p, q) Szász–Mirakyan operators. We have also derived its Korovkin-type approximation properties and rate of convergence.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. T. Acar, \((p, q)\)-generalization of Szász–Mirakyan operators. Math. Methods Appl. Sci. 39(10), 2685–2695 (2016)

    Google Scholar 

  2. T. Acar, P.N. Agrawal, A.S. Kumar, On a modification of \( (p, q)\)-Szász–Mirakyan operators. Complex Anal. Oper. Theory 12(1), 155–167 (2018)

    Article  MathSciNet  Google Scholar 

  3. T. Acar, M. Mursaleen, S.A. Mohiuddine, Stancu type \((p,q)\)-Szász–Mirakyan–Baskakov operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 67(1), 116–128 (2018)

    Google Scholar 

  4. T. Acar, S.A. Mohiuddine, M. Mursaleen, Approximation by \( (p,q)\)-Baskakov–Durrmeyer–Stancu operators. Complex Anal. Oper. Theory 12(6), 1453–1468 (2018).

    Google Scholar 

  5. A. Aral, A generalization of Szász–Mirakyan operators based on \(q\)-integers. Math. Comput. Model. 47(9–10), 1052–1062 (2008)

    Article  Google Scholar 

  6. M. Örkcü, O. Doğru, Weighted statistical approximation by Kantorovich type q-Szász–Mirakyan operators. Appl. Math. Comput. 217(20), 7913–9 (2011)

    Article  MathSciNet  Google Scholar 

  7. R.A. Devore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)

    Book  Google Scholar 

  8. A.D. Gadzhiev, The convergence problem for a sequence of linear positive operators on unbounded sets and theorems analogous to that P. P. Korovkin. Sov. Math. Dokl. 15(5), 1433–1436 (1974)

    Google Scholar 

  9. V. Gupta, A. Aral, Convergence of the \(q\)-analogue of Szász–Beta operators. Appl. Math. Comput. 216(2), 374–380 (2010)

    Google Scholar 

  10. M. Mursaleen, A.A.H. Al-Abied, A. Alotaibi, On \((p, q)\)-Szász–Mirakyan operators and their approximation properties. J. Inequalities Appl. 2017(1), 196 (2017)

    Google Scholar 

  11. M. Mursaleen, A. Al-Abied, M. Nasiruzzaman, Modified \((p, q)\) -Bernstein–Schurer operators and their approximation properties. Cogent Math. 3(1), 1236534 (2016)

    Google Scholar 

  12. M. Mursaleen, A. Al-Abied, K.J. Ansari, Rate of convergence of Chlodowsky type Durrmeyer Jakimovski–Leviatan operators. Tbil. Math. J. 10(2), 173–184 (2017)

    Article  MathSciNet  Google Scholar 

  13. M. Mursaleen, K.J. Ansari, On Chlodowsky variant of Szász operators by Brenke type polynomials. Appl. Math. Comput. 271, 991–1003 (2015)

    MathSciNet  Google Scholar 

  14. M. Mursaleen, K.J. Ansari, A. Khan, On \((p,q)\)-analogue of Bernstein operators. Appl. Math. Comput. 266, 874–882 (2015) [Erratum: Appl. Math. Comput. 278, 70–71 (2016)]

    Google Scholar 

  15. M. Mursaleen, K.J. Ansari, A. Khan, Some approximation results by \((p,q)\)-analogue of Bernstein–Stancu operators, Appl. Math. Comput. 264, 392–402 (2015) [Corrigendum: Appl. Math. Comput. 269, 744–746 (2015)]

    Google Scholar 

  16. M. Mursaleen, K.J. Ansari, A. Khan, Some approximation results for Bernstein–Kantorovich operators based on \((p,q)\)-calculus. U.P.B. Sci. Bull. Ser. A 78(4), 129–142 (2016)

    MathSciNet  Google Scholar 

  17. M. Mursaleen, F. Khan, A. Khan, Approximation by \((p, q)\) -Lorentz polynomials on a compact disk. Complex Anal. Oper. Theory 10(8), 1725–1740 (2016)

    Article  MathSciNet  Google Scholar 

  18. M. Mursaleen, M. Nasiruzzaman, A.A.H. Al-Abied, Dunkl generalization of \(q\)-parametric Szász–Mirakyan operators. Int. J. Anal. Appl. 13(2), 206–215 (2017). ISSN 2291-8639

    Google Scholar 

  19. M. Mursaleen, M. Nasiruzzaman, A. Nurgali, Some approximation results on Bernstein–Schurer operators defined by \((p, q)\) -integers. J. Inequalities Appl. 2015(1), 249 (2015)

    Google Scholar 

  20. M. Mursaleen, M. Nasiruzzaman, A. Khan, K.J. Ansari, Some approximation results on Bleimann–Butzer–Hahn operators defined by \( (p,q)\)-integers. Filomat 30(3), 639–648 (2016)

    Article  MathSciNet  Google Scholar 

  21. M. Mursaleen, M. Nasiruzzaman, N. Ashirbayev, A. Abzhapbarov, Higher order generalization of Bernstein type operators defined by \((p, q)\)-integers. J. Comput. Anal. Appl. 25(5), 817–829 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen & A. A. H. AL-Abied

Authors
  1. M. Mursaleen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. H. AL-Abied
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mursaleen .

Editor information

Editors and Affiliations

  1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    S. A. Mohiuddine

  2. Department of Mathematics, Selçuk University, Selçuklu, Konya, Turkey

    Tuncer Acar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mursaleen, M., AL-Abied, A.A.H. (2018). Approximation Properties of Chlodowsky Variant of (p, q) Szász–Mirakyan–Stancu Operators. In: Mohiuddine, S., Acar, T. (eds) Advances in Summability and Approximation Theory. Springer, Singapore. https://doi.org/10.1007/978-981-13-3077-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation