SavedAdd your journal

Journals / Proceedings of International Mathematical Sciences / 2026 / Volume: 3 Issue: 1

A New Variation on Absolute Summability

Şebnem Yıldız(Ahi Evran University)0000-0003-3763-0308
Pages
—
Publication Date
2021-06-15
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, some new and known results are also obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In [4], Bor has proved a main theorem dealing with absolute weighted arithmetic mean summability factors of infinite series by using a positive non-decreasing sequence.
📊
Key Findings & Data:In this paper, we have extended this result to absolute matrix summability method by using an almost increasing sequence in place of a positive non-decreasing sequence.
💡
Conclusion & Impact:Also, some new and known results are also obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Minkowski · absolute matrix summability · summability factors

Abstract

In [4], Bor has proved a main theorem dealing with absolute weighted arithmetic mean summability factors of infinite series by using a positive non-decreasing sequence. In this paper, we have extended this result to absolute matrix summability method by using an almost increasing sequence in place of a positive non-decreasing sequence. Also, some new and known results are also obtained.

🔖

Cite This Article

Yıldız, Ş. (2021). A New Variation on Absolute Summability. Proceedings of International Mathematical Sciences, Volume: 3 Issue: 1. https://doi.org/10.47086/pims.939184

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (25)

  1. N. K. Bari, S. B. Steckin, Best approximation and differential of two conjugate functions, Trudy. Moskov. Mat. Obsc. 5 (1956) 483-522 (in Russian).
  2. H. Bor, On two summability methods, Math. Proc. Camb. Philos. Soc. 97 (1985) 147-149.
  3. H. Bor, A note on $\left|\bar{N},p_n\right| _k$ summability factors of in nite series, Indian J. Pure Appl. Math. 18 (1987) 330-336.
  4. H. Bor, Factors for absolute weighted arithmetic mean summability of in nite series, Int. J. Anal. Appl. 14 (2017) 175-179.
  5. H. Bor, An application of quasi-monotone sequences to in nite series and Fourier series, Anal. Math. Phys. 8 (2018) 7783.
  6. H. Bor, On absolute summability of factored in nite series and trigonometric Fourier series, Results Math. 73 (2018) 116.
  7. H. Bor, On absolute Riesz summability factors of in nite series and their application to Fourier series, Georgian Math. J. 26 (2019) 361366.
  8. H. Bor, Certain new factor theorems for in nite series and trigonometric Fourier series, Quaest. Math. 43 (2020) 441448
  9. E. Cesaro, Sur la multiplication des series, Bull. Sci. Math. 14 (1890) 114-120.
  10. T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc. 7 (1957) 113-141.
  11. G. H. Hardy, Divergent Series, Clarendon Press. Oxford, (1949).
  12. K. N. Mishra, On the absolute Norlund summability factors of in nite series, Indian J. Pure Appl. Math. 14 (1983) 40-43.
  13. K. N. Mishra and R. S. L. Srivastava, On the absolute Cesaro summability factors of in nite series, Portugal Math. 42 (1983/84) 53-61.
  14. K. N. Mishra and R. S. L. Srivastava, On j N; pnj summability factors of in nite series, Indian J. Pure Appl. Math. 15 (1984) 651-656.
  15. H. S.  Ozarslan, T. Kandefer, On the relative strength of two absolute summability methods, J. Comput. Anal. Appl. 11 (2009) 576{583.
  16. B. E. Rhoades, Inclusion theorems for absolute matrix summability methods, J. Math. Anal. Appl. 238 (1999) 82-90.
  17. W. T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an in nite series, IV. Indian J. Pure Appl. Math. 11 (2003) 1547-1557.
  18. S. Yıldız, On application of matrix summability to Fourier series, Math. Methods Appl. Sci. (2018) 664{670.
  19. S. Yıldız, On the absolute matrix summability factors of Fourier series, Math. Notes 103 (2018) 297-303.
  20. S. Yıldız, A matrix application on absolute weighted arithmetic mean summability factors of in nite series, Tibilisi Math. J. 11 (2018) 59-65.
  21. S. Yıldız, On the generalizations of some factors theorems for in nite series and Fourier series, Filomat 33 (2019) 4343-4351.
  22. S. Yıldız, Matrix application of power increasing sequences to in nite series and Fourier series, Ukranian Math. J. 72 (2020) 730-740.
  23. S. Yıldız, A variation on absolute weighted mean summability factors of Fourier series and its conjugate series, Bol. Soc. Parana. Mat. 38 (2020) 105-113.
  24. S. Yıldız, A recent extension of the weighted mean summability of in nite series, J. Appl. Math. Inform. 39 (2021) 117-124.
  25. K. N. Mishra and R. S. L. Srivastava, On j N; pnj summability factors of in nite series, Indian J. Pure Appl. Math. 15 (1984) 651-656.