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AIMS Mathematics

2026, Volume 11, Issue 6: 17022-17038. doi: 10.3934/math.2026697
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Research article

Matrix domain of the second-order $ q $-Cesàro matrix in classical sequence spaces

  • 1.
    Department of Mathematics, Recep Tayyip Erdoğan University, 53100 Rize, Türkiye
  • 2.
    Department of Mathematics, Tokat Gaziosmanpaşa University, 60250 Tokat, Türkiye
  • Published: 12 June 2026

  • MSC : 40C05, 46A45

  • In this paper, we study a second-order $ q $-Cesàro matrix and its matrix domains in the spaces $ c_0 $ and $ c $. We establish basic structural results, including inclusion relations, connections with earlier Cesàro-type sequence spaces, the duals of these spaces, and the associated matrix transformations. Our approach extends known work on $ q $-Cesàro operators and provides a starting point for further investigations of higher-order $ q $-averaging methods in summability theory.

    Citation: Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz. Matrix domain of the second-order $ q $-Cesàro matrix in classical sequence spaces[J]. AIMS Mathematics, 2026, 11(6): 17022-17038. doi: 10.3934/math.2026697

    Related Papers:

  • In this paper, we study a second-order $ q $-Cesàro matrix and its matrix domains in the spaces $ c_0 $ and $ c $. We establish basic structural results, including inclusion relations, connections with earlier Cesàro-type sequence spaces, the duals of these spaces, and the associated matrix transformations. Our approach extends known work on $ q $-Cesàro operators and provides a starting point for further investigations of higher-order $ q $-averaging methods in summability theory.



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    [1] F. Başar, Summability theory and its applications, New York: Chapman and Hall/CRC, 2022. https://doi.org/10.1201/9781003294153
    [2] A. Boukarou, K. Zennir, Mathematical analysis for sciences and engineering: analysis of sequences, numerical series, mathematical functions, asymptotic analysis, Berlin: De Gruyter, 2026.
    [3] A. Wilansky, Summability through functional analysis, Amsterdam: Elsevier, 2000.
    [4] F. Başar, Infinite matrices and Cesàro sequence spaces of non-absolute type, Mathematical Journal of Ibaraki University, 31 (1999), 1–12. https://doi.org/10.5036/mjiu.31.1 doi: 10.5036/mjiu.31.1
    [5] B. Altay, F. Başar, On some Euler sequence spaces of non-absolute type, Ukr. Math. J., 57 (2005), 1–17. https://doi.org/10.1007/s11253-005-0168-9 doi: 10.1007/s11253-005-0168-9
    [6] H. Chebbah, A. Mennouni, K. Zennir, Three methods to solve two classes of integral equations of the second kind, Bol. Soc. Paran. Mat., 40 (2022), 1–8. https://doi.org/10.5269/bspm.46315 doi: 10.5269/bspm.46315
    [7] Y. Yan, D. Cheng, J. Feng, H. Li, J. Yue, Survey on applications of algebraic state space theory of logical systems to finite state machines, Sci. China Inf. Sci., 66 (2023), 111201. https://doi.org/10.1007/s11432-022-3538-4 doi: 10.1007/s11432-022-3538-4
    [8] V. Kac, P. Cheung, Quantum calculus, New York: Springer, 2002. https://doi.org/10.1007/978-1-4613-0071-7
    [9] F. H. Jackson, On $q$-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193–203.
    [10] H. Aktuğlu, Ş. Bekar, $q$-Cesàro matrix and $q$-statistical convergence, J. Comput. Appl. Math., 235 (2011), 4717–4723. https://doi.org/10.1016/j.cam.2010.08.018 doi: 10.1016/j.cam.2010.08.018
    [11] S. Demiriz, A. Şahin, $q$-Cesàro sequence spaces derived by $q$-analogues, Adv. Math., 5 (2016), 97–110.
    [12] T. Yaying, B. Hazarika, M. Mursaleen, On sequence space derived by the domain of $q$-Cesàro matrix in $\ell_p$ space and the associated operator ideal, J. Math. Anal. Appl., 493 (2021), 124453. https://doi.org/10.1016/j.jmaa.2020.124453 doi: 10.1016/j.jmaa.2020.124453
    [13] K. İ. Atabey, M. Çınar, M. Et, New triangular $q$-Fibonacci matrix, Filomat, 39 (2025), 601–615. https://doi.org/10.2298/FIL2502601A doi: 10.2298/FIL2502601A
    [14] K. İ. Atabey, M. Çınar, M. Et, $q$-Fibonacci sequence spaces and related matrix transformations, J. Appl. Math. Comput., 69 (2023), 2135–2154. https://doi.org/10.1007/s12190-022-01825-9 doi: 10.1007/s12190-022-01825-9
    [15] H. B. Ellidokuzoğlu, S. Demiriz, On some generalized $q$-difference sequence spaces, AIMS Mathematics, 8 (2023), 18607–18617. https://doi.org/10.3934/math.2023947 doi: 10.3934/math.2023947
    [16] H. B. Ellidokuzoğlu, S. Demiriz, Some new paranormed sequence spaces derived by $q$-second difference matrix, J. Math. Ext., 17 (2023), 1–18. https://doi.org/10.30495/JME.2023.2766 doi: 10.30495/JME.2023.2766
    [17] H. B. Ellidokuzoğlu, S. Demiriz, M. İ. Kara, $q$-Schröder sequence spaces and Schröder core, Filomat, 39 (2025), 715–729. https://doi.org/10.2298/FIL2502715B doi: 10.2298/FIL2502715B
    [18] M. Çınar, M. Et, $q$-double Cesàro matrices and $q$-statistical convergence of double sequences, Natl. Acad. Sci. Lett., 43 (2020), 73–76. https://doi.org/10.1007/s40009-019-00808-y doi: 10.1007/s40009-019-00808-y
    [19] M. E. Yıldırım, The spectrum and fine spectrum of $q$-Cesàro matrices with $0 < q < 1$ on $c_0$, Numer. Func. Anal. Opt., 41 (2020), 361–377. https://doi.org/10.1080/01630563.2019.1633666 doi: 10.1080/01630563.2019.1633666
    [20] N. Durna, M. E. Türkay, The spectrum of $q$-Cesàro matrices on $c$ and its various spectral decomposition for $0 < q < 1$, Oper. Matrices, 15 (2021), 795–813. https://doi.org/10.7153/oam-2021-15-55 doi: 10.7153/oam-2021-15-55
    [21] S. R. El-Shabrawy, On $q$-Cesàro operators: boundedness, compactness and spectra, Numer. Func. Anal. Opt., 42 (2021), 1019–1037. https://doi.org/10.1080/01630563.2021.1933027 doi: 10.1080/01630563.2021.1933027
    [22] T. Yaying, M. Mursaleen, On Motzkin sequence spaces via $q$-analog and compact operators, Demonstr. Math., 58 (2025), 20250140. https://doi.org/10.1515/dema-2025-0140 doi: 10.1515/dema-2025-0140
    [23] T. Yaying, B. Hazarika, M. Et, On some sequence spaces via $q$-Pascal matrix and its geometric properties, Symmetry, 15 (2023), 1659. https://doi.org/10.3390/sym15091659 doi: 10.3390/sym15091659
    [24] T. Yaying, B. Hazarika, S. A. Mohiuddine, M. Et, On sequence spaces due to $l$th order $q$-difference operator and its spectrum, Iran. J. Sci., 47 (2023), 1271–1281. https://doi.org/10.1007/s40995-023-01487-7 doi: 10.1007/s40995-023-01487-7
    [25] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenräumen eine Ergebnisübersicht, Math. Z., 154 (1977), 1–16. https://doi.org/10.1007/BF01215107 doi: 10.1007/BF01215107
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