Skip to main content
SpringerLink
Log in

On the q-statistical convergence of double sequences

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In this paper, we study q-statistical convergence for double sequences. The definitions of q-analog of statistical Cauchy and statistical pre-Cauchy for double sequences are given. The necessary and sufficient condition for a double sequence to have different statistical limits is also obtained. We show that a q-statistical convergent sequence is q-statistical Cauchy and vice-versa.

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. H. Aktuğlu, Ş Bekar, \(q\)-Cesàro matrix and \(q\)-statistical convergence. Jour. Comput. Appl. Math. 235(16), 4717–4723 (2011)

    Article  Google Scholar 

  2. A.A.H. Al-Abied, M. Ayman Mursaleen, M. Mursaleen, Szász type operators involving Charlier polynomials and approximation properties. Filomat 35(15), 5149–5159 (2021)

    Article  MathSciNet  Google Scholar 

  3. M. Ayman Mursaleen, S. Serra-Capizzano, Statistical convergence via \(q\)-calculus and a KorovkinÂs type approximation theorem. Axioms 11(2), 70 (2022)

    Article  Google Scholar 

  4. Q.-B. Cai, A. Kilicman, M. Ayman Mursaleen, Approximation properties and q-statistical convergence of Stancu type generalized Baskakov–Szász operators. J. Funct. Spaces 2022, 2286500 (2022)

    Google Scholar 

  5. M.-Y. Chen, Md. Nasiruzzaman, M. Ayman Mursaleen, N. Rao, A.A. Kiliçman, On shape parameter a based approximation properties and \(q\)-statistical convergence of Baskakov–Gamma operators. J. Math. 2022, 4190732 (2022)

    Article  MathSciNet  Google Scholar 

  6. M. Çinar, M. Et, \(q\)-double Cesàro matrices and \(q\)-statistical convergence of double sequences. Nat. Acad. Sci. Lett. 43(1), 73–76 (2020)

    Article  MathSciNet  Google Scholar 

  7. J.S. Connor, J. Fridy, J. Kline, Statistically pre-Cauchy sequences. Analysis 14(4), 311–318 (1994)

    Article  MathSciNet  Google Scholar 

  8. J.S. Connor, The statistical and strong \(p\)-Cesàro convergence of sequences. Analysis 8(1–2), 47–63 (1988)

    MathSciNet  Google Scholar 

  9. H. Fast, Sur la convergence statistique. Colloq. Math. 2(3–4), 241–244 (1951)

    Article  MathSciNet  Google Scholar 

  10. A. Freedman, J. Sember, Densities and summability. Pac. J. Math. 95(2), 293–305 (1981)

    Article  MathSciNet  Google Scholar 

  11. J.A. Fridy, On stastistical convergence. Analysis 5, 301–313 (1985)

    Article  MathSciNet  Google Scholar 

  12. V. Kac, P. Cheung, Quantum Calculus. Universitext (Springer, New York, 2002)

    Book  Google Scholar 

  13. F. Móricz, Statistical convergence of multiple sequences. Arch. Math. 81(1), 82–89 (2003)

    Article  MathSciNet  Google Scholar 

  14. M. Mursaleen, O.H.H. Edely, Statistical convergence of double sequences. J. Math. Anal. Appl. 288, 223–231 (2003)

    Article  MathSciNet  Google Scholar 

  15. M. Mursaleen, S. Tabassum, R. Fatma, On q-statistical summability method and its properties. Iran. J. Sci. Technol. Trans. Sci. 46(2), 455–460 (2022)

    Article  MathSciNet  Google Scholar 

  16. M. Nasiruzzaman, A. Kiliçman, M. Ayman-Mursaleen, Construction of q-Baskakov operators by wavelets and approximation properties. Iran. J. Sci. Technol. Trans. Sci. 46(5), 1495–1503 (2022)

    Article  MathSciNet  Google Scholar 

  17. T. Šalát, On statistically convergent sequences of real numbers. Math. Slovaca 30(2), 139–150 (1980)

    MathSciNet  Google Scholar 

  18. I.J. Schoenberg, The integrability of certain functions and related summability methods. Am. Math. Mon. 66(5), 361–375 (1959)

    Article  MathSciNet  Google Scholar 

  19. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2(1), 73–74 (1951)

    MathSciNet  Google Scholar 

  20. O. Toeplitz, Über allgemeine lineare Mittelbildungen. Prace Matematyczno-Fizyczne 22(1), 113–119 (1911)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

    Mohammad Mursaleen

  2. University Centre for Research and Development, Chandigarh University, Mohali, 140243, Punjab, India

    Mohammad Mursaleen

  3. Department of Applied Mathematics, Zakir Husain College of Engineering and Technology, Aligarh Muslim University, Aligarh, 202002, India

    Sabiha Tabassum & Ruqaiyya Fatma

Authors
  1. Mohammad Mursaleen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sabiha Tabassum
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruqaiyya Fatma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Mursaleen.

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

Mursaleen, M., Tabassum, S. & Fatma, R. On the q-statistical convergence of double sequences. Period Math Hung (2024). https://doi.org/10.1007/s10998-023-00556-z

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10998-023-00556-z

Keywords

Mathematics Subject Classification

Search

Navigation