Research Article
Year 2025,
Volume: 74 Issue: 2, 191 - 199, 19.06.2025
Abstract
References
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- Bose, K., Das, P., Sengupta, S., On spliced sequences and the density of points with respect to a matrix constructed by using a weight function, Ukrainian Mathematical Journal, 71 (2020), 1359–1374. https://doi.org/10.1007/s11253-020-01720-1.
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- Hamilton, H. J., Transformations of multiple sequences, Duke Mathematical Journal, 2 (1936), 29–60.
- Mursaleen, E., Osama, H. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231.
- Osikiewicz, J. A., Summability of spliced sequences, Rocky Mountain J. Math., 35 (2005), 977–996.
- Patterson, R. F., Analogues of some fundamental theorems of summability theory, International Journal of Mathematics and Mathematical Sciences, 23 (2000), 1–9.
- Patterson, R. F., Lemma, M., Four dimensional matrix characterization of double oscillation via RH-conservative and RH-multiplicative matrices, Cent. Eur. J. Math., 6 (2008), 581–594. https://doi.org/10.2478/s11533-008-0043-7.
- Pringsheim, A., On the theory of doubly infinite sequences of numbers, Math. Ann., 53 (1900), 289–321.
- Robinson, G. M., Divergent double sequences and series, Transactions of the American Mathematical Society, 28 (1926), 50–73.
- Ünver, M., Abel summability in topological spaces, Monatshefte f¨ur Mathematik, 178 (2015), 633–643. https://doi.org/10.1007/s00605-014-0717-0.
- Ünver, M., Khan, M. K., Orhan, C., A-distributional summability in topological spaces, Positivity, 18 (2014), 131–145. https://doi.org/10.1007/s11117-013-0235-7.
- Yardımcı, Ş., Gülfırat, M., Spliced sequences and summability with a rate, Positivity 27(17) (2023). https://doi.org/10.1007/s11117-023-00970-0.
- Yurdakadim, T., Ünver, M., Some results concerning the summability of spliced sequences, Turk. J. Math., 40 (2016), 1134–1143. https://doi.org/10.3906/mat-1508-34.
Year 2025,
Volume: 74 Issue: 2, 191 - 199, 19.06.2025
Abstract
In this paper, we introduce spliced double sequences and give the summability of this new notion by using four dimensional matrices. Note that there are some examples which show the effectiveness of spliced double sequences in summability theory.
References
- Bartoszewicz, A., Das, P., Gła̧b, S., On matrix summability of spliced sequences and A-density of points, Linear Algebra Appl., 487 (2015), 22–42. https://doi.org/10.1016/j.laa.2015.08.031.
- Bose, K., Das, P., Sengupta, S., On spliced sequences and the density of points with respect to a matrix constructed by using a weight function, Ukrainian Mathematical Journal, 71 (2020), 1359–1374. https://doi.org/10.1007/s11253-020-01720-1.
- Gökhan, A., Çolak, R., Mursaleen, M., Some matrix transformation and generalized core of double sequences, Mathematical and Computer Modelling, 49 (2009), 1721–1731. https://doi.org/10.1016/j.mcm.2008.12.002.
- Hamilton, H. J., Transformations of multiple sequences, Duke Mathematical Journal, 2 (1936), 29–60.
- Mursaleen, E., Osama, H. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231.
- Osikiewicz, J. A., Summability of spliced sequences, Rocky Mountain J. Math., 35 (2005), 977–996.
- Patterson, R. F., Analogues of some fundamental theorems of summability theory, International Journal of Mathematics and Mathematical Sciences, 23 (2000), 1–9.
- Patterson, R. F., Lemma, M., Four dimensional matrix characterization of double oscillation via RH-conservative and RH-multiplicative matrices, Cent. Eur. J. Math., 6 (2008), 581–594. https://doi.org/10.2478/s11533-008-0043-7.
- Pringsheim, A., On the theory of doubly infinite sequences of numbers, Math. Ann., 53 (1900), 289–321.
- Robinson, G. M., Divergent double sequences and series, Transactions of the American Mathematical Society, 28 (1926), 50–73.
- Ünver, M., Abel summability in topological spaces, Monatshefte f¨ur Mathematik, 178 (2015), 633–643. https://doi.org/10.1007/s00605-014-0717-0.
- Ünver, M., Khan, M. K., Orhan, C., A-distributional summability in topological spaces, Positivity, 18 (2014), 131–145. https://doi.org/10.1007/s11117-013-0235-7.
- Yardımcı, Ş., Gülfırat, M., Spliced sequences and summability with a rate, Positivity 27(17) (2023). https://doi.org/10.1007/s11117-023-00970-0.
- Yurdakadim, T., Ünver, M., Some results concerning the summability of spliced sequences, Turk. J. Math., 40 (2016), 1134–1143. https://doi.org/10.3906/mat-1508-34.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 19, 2025 |
| Submission Date | March 7, 2024 |
| Acceptance Date | January 23, 2025 |
| Published in Issue | Year 2025 Volume: 74 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
