On $\left| T,\delta \right|_{k}$ summability of factored Fourier series

Şebnem Yıldız Yar

doi:10.47086/pims.1781470

On $\left| T,\delta \right|_{k}$ summability of factored Fourier series

Abstract

Some results on the absolute matrix summability of factored Fourier series have recently been obtained by Sarıgöl (see \cite{Sara}). In this present paper, we extend his results to $\left| T,\delta \right|_{k}$ summability.

Keywords

References

H. Bor, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), 147–149.
H. Bor, On local property of |¯N, pn; δ|k summability of factored Fourier series, J. Math. Anal. Appl. 179 (1993), 646–649.
H. Bor, A note on local property of factored Fourier series, J. Non. Anal. 64 (2006), 513–517.
H. Bor, Some new results on absolute Riesz summability of infinite series and Fourier series, Positivity 20 (2016), 599–605.
H. Bor, An application of quasi-monotone sequences to infinite series and Fourier series, Anal. Math. Phys. 8 (2018), 77-–83.
H. Bor, On absolute Riesz summability factors of infinite series and their application to Fourier series, Georgian Math. J. 26(3) (2019), 361–366.
H. Bor, Certain new factor theorems for infinite series and trigonometric fourier series, Quaestiones Mathematicae 43(4) (2020), 441—448 https://doi.org/10.2989/16073606.2019.1578836
H. Bor, A new note on factored infinite series and trigonometric Fourier series, Comptes Rendus. Math´ematique 359(3) (2021), 323–328.

H. Bor, Factored infinite series and Fourier series involving almost increasing sequences, Bull. Sci. Math. 169 (2021), 102990.
H. Bor, Absolute weighted arithmetic mean summability of factored infinite series and Fourier series, Bulletin des Sciences Math´ematiques 176 (2022), 103116.
L. S. Bosanquet, Note on the absolute summability (C) of a Fourier series, J. London Math.Soc. 11(1) (1936), 11–15.
K. K. Chen, Functions of bounded variation and the Ces`aro means of Fourier series, Acad. Sinica Sci. Record 1 (1945), 283–289.
T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 37 (1957), 113-141.
G. H. Hardy, Divergent Series, Oxford Univ. Press., Oxford, (1949).
M. Izumi and S. Izumi, Absolute N¨orlund summability factor of Fourier series. Proc. Japan Acad. 46 (1970), 642–646.
B. B.Jena, S.K.,Paikray and U.K.Misra, On generalized local property of |A, δ|k summability of factored Fourier series, Inter. J. Anal. Appl. 16(2) (2018), 209–221.
K.Kanno, On the absolute N¨orlund summability of the factored Fourier series, Tohoku Math. J. 21(3) (1969), 434–447.
D.S. Yu and P. Zhou, A new class of matrices and its applications to absolute summability factor theorems, Math. Comput. Model. 57 (2013), 401–412.
E.C. Tichmarsh, The theory of functions, Oxford University Press, London, (1961).
A.Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, vol 1, 81959.
M.A. Sarıg¨ol, On local property of |A|k summability of factored Fourier series, J. Math. Anal. Appl. 188 (1994), 118–127.
M. A. Sarıg¨ol, On the local properties of factored Fourier series, Appl. Math. Comp. 216 (2010), 3386- 3390.
M. A. Sarıg¨ol, On |A|k summability of factorable Fourier series, Trans. A. Raz. Math. Inst. 178 (2024), 137–143.
S. Yildiz, On application of matrix summability to Fourier series, Math. Meth. Appl. Sci. 41(2) (2018), 664–670.
S. Yildiz, On absolute matrix summability factors of infinite series and Fourier series, Bull. Sci. Math. 170 (2021), 103000.
S. Yildiz, On the generalizations of some factors theorems for infinite series and Fourier series, Filomat 33(14) (2019), 4343–4351.
S. Yildiz, On the absolute matrix summability factors of Fourier series, Math. Notes 103(1-2) (2018), 297–303.
W. T. Sulaiman, On some summability factors of infinite series, Proc. Amer. Math. Soc. 115 (1992), 313– 317.

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Şebnem Yıldız Yar ^*
0000-0003-3763-0308
Türkiye

Publication Date

January 3, 2026

Submission Date

September 10, 2025

Acceptance Date

November 13, 2025

Published in Issue

Year 2025 Volume: 7 Number: 2

DOI

https://doi.org/10.47086/pims.1781470

IZ

https://izlik.org/JA89EK63GX

Cite

RIS / Bibtex

APA

Yıldız Yar, Ş. (2026). On $\left| T,\delta \right|_{k}$ summability of factored Fourier series. Proceedings of International Mathematical Sciences, 7(2), 46-53. https://doi.org/10.47086/pims.1781470

AMA

1.Yıldız Yar Ş. On $\left| T,\delta \right|_{k}$ summability of factored Fourier series. PIMS. 2026;7(2):46-53. doi:10.47086/pims.1781470

Chicago

Yıldız Yar, Şebnem. 2026. “On $\left| T,\delta \right|_{k}$ Summability of Factored Fourier Series”. Proceedings of International Mathematical Sciences 7 (2): 46-53. https://doi.org/10.47086/pims.1781470.

EndNote

Yıldız Yar Ş (January 1, 2026) On $\left| T,\delta \right|_{k}$ summability of factored Fourier series. Proceedings of International Mathematical Sciences 7 2 46–53.

IEEE

[1]Ş. Yıldız Yar, “On $\left| T,\delta \right|_{k}$ summability of factored Fourier series”, PIMS, vol. 7, no. 2, pp. 46–53, Jan. 2026, doi: 10.47086/pims.1781470.

ISNAD

Yıldız Yar, Şebnem. “On $\left| T,\delta \right|_{k}$ Summability of Factored Fourier Series”. Proceedings of International Mathematical Sciences 7/2 (January 1, 2026): 46-53. https://doi.org/10.47086/pims.1781470.

JAMA

1.Yıldız Yar Ş. On $\left| T,\delta \right|_{k}$ summability of factored Fourier series. PIMS. 2026;7:46–53.

MLA

Yıldız Yar, Şebnem. “On $\left| T,\delta \right|_{k}$ Summability of Factored Fourier Series”. Proceedings of International Mathematical Sciences, vol. 7, no. 2, Jan. 2026, pp. 46-53, doi:10.47086/pims.1781470.

Vancouver

1.Şebnem Yıldız Yar. On $\left| T,\delta \right|_{k}$ summability of factored Fourier series. PIMS. 2026 Jan. 1;7(2):46-53. doi:10.47086/pims.1781470