Skip to main content
SpringerLink
Log in

A new application of almost increasing sequences to infinite series and Fourier series

  • Published:
Analysis and Mathematical Physics Aims and scope Submit manuscript

Abstract

Recently, we have obtained two general theorems dealing with \(|\bar{N},p_{n}|_{k}\) summability factors of infinite series and trigonometric Fourier series (Bor in Bull Sci Math 169:102990, 2021) by using almost increasing sequences. In this paper, we have generalized these theorems to \(|\bar{N},p_n;\theta _{n}|_{k}\) summability methods. Some new and known results are also obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bari, N.K., Ste\(\check{c}\)kin, S.B.: Best approximation and differential properties of two conjugate functions. Trudy. Moskov. Mat. Ob\(\check{s}\)\(\check{c}\). 5, 483–522 (1956) (in Russian)

  2. Bhatt, S.N.: An aspect of local propert of \(\left|R, logn,1\right|\) summability of Fourier series. Tôhoku Math. J. 2(11), 13–19 (1959)

    Google Scholar 

  3. Bor, H.: On two summability methods. Math. Proc. Cambr. Philos. Soc. 97, 147–149 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bor, H.: On the relative strength of two absolute summability methods. Proc. Am. Math. Soc. 113, 1009–1012 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bor, H.: An application of quasi-monotone sequences to infinite series and Fourier series. Anal. Math. Phys. 8, 77–83 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bor, H.: On absolute Riesz summability factors of infinite series and their application to Fourier series. Georgian Math. J. 26, 361–366 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bor, H.: Certain new factor theorems for infinite series and trigonometric Fourier series. Quaest. Math. 43, 441–448 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bor, H.: A new note on factored infinite series and trigonometric Fourier series. C. R. Math. Acad. Sci. Paris 359, 323–328 (2021)

    MathSciNet  MATH  Google Scholar 

  9. Bor, H.: Factored infinite series and Fourier series involving almost increasing sequences. Bull. Sci. Math. 169, 102990 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bor, H.: A new application of a wider class of power increasing sequences. Numer. Funct. Anal. Optim. 42, 712–720 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bor, H.: Absolute weighted arithmetic mean summability of factored infinite series and Fourier series. Bull. Sci. Math. 176, 103116 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bor, H.: On absolute weighted arithmetic mean summability of infinite series and Fourier series. Proc. Am. Math. Soc. 150, 3517–3523 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cesàro, E.: Sur la multiplication des séries. Bull. Sci. Math. 14, 114–120 (1890)

    MATH  Google Scholar 

  14. Chen, K.K.: Functions of bounded variation and the Cesàro means of Fourier series. Acad. Sin. Sci. Record 1, 283–289 (1945)

    Google Scholar 

  15. Flett, T.M.: On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. Lond. Math. Soc. 7, 113–141 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hardy, G.H.: Divergent Series. Clarendon Press, Oxford (1949)

    MATH  Google Scholar 

  17. Mazhar, S.M.: Absolute summability factors of infinite series. Kyungpook Math. J. 39, 67–73 (1999)

    MathSciNet  MATH  Google Scholar 

  18. Persson, L.E., Tephnadze, G., Weisz, F.: Martingale Hardy Spaces and Summability of one-dimensional Vilenkin–Fourier Series, Springer, Berlin (2022)

  19. Sulaiman, W.T.: On some summability factors of infinite series. Proc. Am. Math. Soc. 115, 313–317 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sunouchi, G.: Notes on Fourier analysis XVIII. Absolute summability of series with constant terms. Tôhoku Math. J. 2(1), 57–65 (1949)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author expresses his sincerest thanks to referee for his/her valuable suggestions for the improvement of this paper.

Author information

Authors and Affiliations

  1. P.O. Box 121, TR-06502, Bahçelievler, Ankara, Turkey

    Hüseyin Bor

Authors
  1. Hüseyin Bor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hüseyin Bor.

Ethics declarations

Conflict of interest

The author declare that there is conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bor, H. A new application of almost increasing sequences to infinite series and Fourier series. Anal.Math.Phys. 13, 89 (2023). https://doi.org/10.1007/s13324-023-00854-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13324-023-00854-2

Keywords

Mathematics Subject Classification

Search

Navigation