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Journals / Proceedings of International Mathematical Sciences / 2025 / Volume: 7 Issue: 2

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

Şebnem Yıldız Yar(ORDU UNIVERSITY)0000-0003-3763-0308
Pages
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Publication Date
2026-01-03
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In this present paper, we extend his results to $\left| T,\delta \right|_{k}$ summability.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Some results on the absolute matrix summability of factored Fourier series have recently been obtained by Sarıgöl (see \cite{Sara}).
📊
Key Findings & Data:Some results on the absolute matrix summability of factored Fourier series have recently been obtained by Sarıgöl (see \cite{Sara}).
💡
Conclusion & Impact:In this present paper, we extend his results to $\left| T,\delta \right|_{k}$ summability.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:matrix summability · summability factor · infinite 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.

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Cite This Article

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

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References (28)

  1. H. Bor, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), 147–149.
  2. H. Bor, On local property of |¯N, pn; δ|k summability of factored Fourier series, J. Math. Anal. Appl. 179 (1993), 646–649.
  3. H. Bor, A note on local property of factored Fourier series, J. Non. Anal. 64 (2006), 513–517.
  4. H. Bor, Some new results on absolute Riesz summability of infinite series and Fourier series, Positivity 20 (2016), 599–605.
  5. H. Bor, An application of quasi-monotone sequences to infinite series and Fourier series, Anal. Math. Phys. 8 (2018), 77-–83.
  6. H. Bor, On absolute Riesz summability factors of infinite series and their application to Fourier series, Georgian Math. J. 26(3) (2019), 361–366.
  7. 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
  8. H. Bor, A new note on factored infinite series and trigonometric Fourier series, Comptes Rendus. Math´ematique 359(3) (2021), 323–328.
  9. H. Bor, Factored infinite series and Fourier series involving almost increasing sequences, Bull. Sci. Math. 169 (2021), 102990.
  10. H. Bor, Absolute weighted arithmetic mean summability of factored infinite series and Fourier series, Bulletin des Sciences Math´ematiques 176 (2022), 103116.
  11. L. S. Bosanquet, Note on the absolute summability (C) of a Fourier series, J. London Math.Soc. 11(1) (1936), 11–15.
  12. K. K. Chen, Functions of bounded variation and the Ces`aro means of Fourier series, Acad. Sinica Sci. Record 1 (1945), 283–289.
  13. T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 37 (1957), 113-141.
  14. G. H. Hardy, Divergent Series, Oxford Univ. Press., Oxford, (1949).
  15. M. Izumi and S. Izumi, Absolute N¨orlund summability factor of Fourier series. Proc. Japan Acad. 46 (1970), 642–646.
  16. 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.
  17. K.Kanno, On the absolute N¨orlund summability of the factored Fourier series, Tohoku Math. J. 21(3) (1969), 434–447.
  18. 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.
  19. E.C. Tichmarsh, The theory of functions, Oxford University Press, London, (1961).
  20. A.Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, vol 1, 81959.
  21. M.A. Sarıg¨ol, On local property of |A|k summability of factored Fourier series, J. Math. Anal. Appl. 188 (1994), 118–127.
  22. M. A. Sarıg¨ol, On the local properties of factored Fourier series, Appl. Math. Comp. 216 (2010), 3386- 3390.
  23. M. A. Sarıg¨ol, On |A|k summability of factorable Fourier series, Trans. A. Raz. Math. Inst. 178 (2024), 137–143.
  24. S. Yildiz, On application of matrix summability to Fourier series, Math. Meth. Appl. Sci. 41(2) (2018), 664–670.
  25. S. Yildiz, On absolute matrix summability factors of infinite series and Fourier series, Bull. Sci. Math. 170 (2021), 103000.
  26. S. Yildiz, On the generalizations of some factors theorems for infinite series and Fourier series, Filomat 33(14) (2019), 4343–4351.
  27. S. Yildiz, On the absolute matrix summability factors of Fourier series, Math. Notes 103(1-2) (2018), 297–303.
  28. W. T. Sulaiman, On some summability factors of infinite series, Proc. Amer. Math. Soc. 115 (1992), 313– 317.