Skip to main content
Log in

An Application of Almost Increasing Sequences

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

In this paper, a general theorem on absolute Cesàro summability of an infinite series is proved by using an almost increasing sequence instead of a positive non-decreasing sequence

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Cesàro E. "Sur la multiplication des séries", Bull. Sci. Math. 14, 114-120 (1890).

    MATH  Google Scholar 

  2. Pati T. "The summability factors of infinite series", Duke Math. J. 21, 271-283 (1954).

    Article  MathSciNet  Google Scholar 

  3. Seyhan H. "On the generalized Cesàro summability factors", Acta Comment. Univ. Tartu Math. 3, 3-6 (1999).

    MathSciNet  MATH  Google Scholar 

  4. Flett T.M. "Some more theorems concerning the absolute summability of Fourier series and power series", Proc. London Math. Soc. (3) 8, 357-387 (1958).

    Article  MathSciNet  Google Scholar 

  5. Flett T.M. "On an extension of absolute summability and some theorems of Littlewood and Paley", Proc. London Math. Soc. (3) 7, 113-141 (1957).

    Article  MathSciNet  Google Scholar 

  6. Bor H. "On the absolute Cesàro summability factors", Anal. Numér. Théor. Approx. 20 (1–2), 11-14 (1991).

    MathSciNet  MATH  Google Scholar 

  7. Bor H., Özarslan H.S. "A note on absolute summability factors", Adv. Stud. Contemp. Math. 6 (1), 1-11 (2003).

    MathSciNet  MATH  Google Scholar 

  8. Bor H., Seyhan H. "A note on almost increasing sequences", Comment. Math. Prace Mat. 39, 37-42 (1999).

    MathSciNet  MATH  Google Scholar 

  9. Özarslan H.S. "On the generalized Cesàro summability factors", Acta Math. Acad. Paedagog. Nyházi. 17 (1), 3-7 (2001).

    MathSciNet  MATH  Google Scholar 

  10. Özarslan H.S. "Factors for the \(\varphi-\left|C,\alpha \right|_{k}\) summability", Adv. Stud. Contemp. Math. 5 (1), 25-31 (2002).

    MathSciNet  Google Scholar 

  11. Özarslan H.S. "A note on absolute summability factors", Proc. Indian Acad. Sci. Math. Sci. 113 (2), 165-169 (2003).

    Article  MathSciNet  Google Scholar 

  12. Özarslan H.S. "Absolute Cesàro summability factors", J. Concr. Appl. Math. 5 (3), 231-236 (2007).

    MathSciNet  MATH  Google Scholar 

  13. Özarslan H.S. "On absolute Cesàro summability factors of infinite series", Commun. Math. Anal. 3 (1), 53-56 (2007).

    MathSciNet  MATH  Google Scholar 

  14. Özarslan H.S. "A note on generalized absolute Cesàro summability", J. Comp. Anal. Appl. 12 (3), 581-585 (2010).

    MATH  Google Scholar 

  15. Seyhan H. "A note on summability methods", Math. Slovaca 49 (2), 201-208 (1999).

    MathSciNet  MATH  Google Scholar 

  16. Bari N.K., Stečkin S.B. "Best approximations and differential properties of two conjugate functions", Trudy Moskov. Mat. Obšč. 5, 483-522 (1956) [in Russian].

    MathSciNet  Google Scholar 

  17. Bosanquet L.S. "A mean value theorem", J. London Math. Soc. 16, 146-148 (1941).

    Article  MathSciNet  Google Scholar 

  18. Mazhar S.M. "A note on absolute summability factors", Bull. Inst. Math. Acad. Sinica 25, 233-242 (1997).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. Kartal.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 11, pp. 16–20.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kartal, B. An Application of Almost Increasing Sequences. Russ Math. 65, 14–17 (2021). https://doi.org/10.3103/S1066369X21110025

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X21110025

Keywords

Navigation