Advertisement

Mathematical Notes

, Volume 103, Issue 1–2, pp 297–303 | Cite as

On the Absolute Matrix Summability Factors of Fourier Series

  • Ş. Yıldız
Article

Abstract

In this paper, two known theorems on |, p n | k summability methods of Fourier series have been generalized for |A, p n | k summability factors of Fourier series by using different matrix transformations. New results have been obtained dealing with some other summability methods.

Keywords

Summability factors absolute matrix summability Fourier series infinite series Ho¨ lder inequality Minkowski inequality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Bor, “On two summability methods,” Math. Proc. Cambridge Philos. Soc. 97, 147–149 (1985).CrossRefMATHGoogle Scholar
  2. 2.
    H. Bor, “Multipliers for N, pn k summability of Fourier series,” Bull. Inst. Math. Acad. Sinica 17, 285–290 (1989).MATHGoogle Scholar
  3. 3.
    H. Bor, “On the local property of N, pn k summability of factored Fourier series,” J. Math. Anal. Appl. 163, 220–226 (1992).CrossRefMATHGoogle Scholar
  4. 4.
    H. Bor, “On local property of N, pn; dk summability of factored Fourier series,” J. Math. Anal. Appl. 179, 646–649 (1993).CrossRefMATHGoogle Scholar
  5. 5.
    H. Bor, “On the local property of factored Fourier series,” Z. Anal. Adwend. 16, 769–773 (1997).CrossRefMATHGoogle Scholar
  6. 6.
    H. Bor, “Factors for N, pn, ?n k summability of Fourier series,” Bull. Inst. Math. Acad. Sin. (N. S.) 3, 399–406 (2008).MATHGoogle Scholar
  7. 7.
    H. Bor, “A note on factored Fourier series,” J. Comput. Anal. Appl. 4 (11), 748–753 (2009).MATHGoogle Scholar
  8. 8.
    H. Bor, “On local properties of factored Fourier series,” Kyungpook Math. J. 49 (2), 313–319 (2009).CrossRefMATHGoogle Scholar
  9. 9.
    H. Bor, “On the localization of factored Fourier series,” Acta Univ. Apulensis Math. Inform. 24, 239–245 (2010).MATHGoogle Scholar
  10. 10.
    H. Bor, D. S. Yu and P. Zhou, ”On local property of absolute summability of factored Fourier series,” Filomat 28, 1675–1686 (2014).CrossRefMATHGoogle Scholar
  11. 11.
    H. Bor, “Some new results on infinite series and Fourier series,” Positivity 19, 467–473 (2015).CrossRefMATHGoogle Scholar
  12. 12.
    H. Bor, “On absolute weighted mean summability of infinite series and Fourier series,” Filomat 30, 2803–2807 (2016).CrossRefMATHGoogle Scholar
  13. 13.
    H. Bor, “Some new results on absolute Riesz summability of infinite series and Fourier series,” Positivity 20, 599–605 (2016).CrossRefMATHGoogle Scholar
  14. 14.
    H. Bor, “A new summability factor theorem for trigonometric Fourier series,” Bull. Math. Anal. Appl. 8, 67–71 (2016).Google Scholar
  15. 15.
    G. H. Hardy, “Divergent Series,” Oxford University Press Oxford (1949).Google Scholar
  16. 16.
    T. M. Flett, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. Lond. Math. Soc. 7, 113–141 (1957).CrossRefMATHGoogle Scholar
  17. 17.
    K. N. Mishra, “Multipliers for N, pn summability of Fourier series,” Bull. Inst. Math. Acad. Sinica 14, 431–438 (1986).MATHGoogle Scholar
  18. 18.
    H. S. Özarslan and S. Yildiz, “A new study on the absolute summability factors of Fourier series,” J. Math. Anal. 7, 31–36 (2016).MATHGoogle Scholar
  19. 19.
    W. T Sulaiman, “Inclusion theorems for absolute matrix summabilitymethods of an infinite series,” IV Indian J. Pure Appl. Math. 34 (11), 1547–1557 (2003).MATHGoogle Scholar
  20. 20.
    N. Tanovicc-Miller, “On strong summability,” Glas. Mat. 34 (14), 87–97 (1979).Google Scholar
  21. 21.
    S. Yıldız, “A new theorem on local properties of factored Fourier series,” Bull. Math. Anal. Appl. 8 (2), 1–8 (2016).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsAhi Evran UniversityKırşehirTurkey

Personalised recommendations