BibTex RIS Kaynak Göster

On strongly deferred Cesaro summability and deferred statistical convergence of the sequences

Yıl 2013, , 22 - 25, 23.06.2013

Mehmet Kucukaslan Mujde Yılmazturk

https://doi.org/10.17678/beuscitech.47136

Öz

In this paper, it is shown that, if the sequence is strongly deferred Cesaro summable for any , then it must be deferred statistically convergent and the inverse is also satisfied when the sequence is bounded.

Anahtar Kelimeler

Summability of sequences strongly summable sequence statistical convergence

Kaynakça

  • Agnew RP (1932). On deferred Cesaro Mean. Comm Ann Math, 33, 413-421.
  • Armitage DH, Maddox IJ (1989) A new type of Cesaro Mean. Analysis 9,195-204.
  • Buck RC (1953). Generalized asymptotic Density. Amer Math Comm 75, 335-346.
  • Connor JS (1988). The statistical and strong p-Cesaro of sequences. Analysis 847-63.
  • Connor JS (1989). On strong matrix summability with respect to a modulus and statistical convergence. Can Math Bull 32, 194-198.
  • Erdös P, Tenenbaum G (1989). Sur les densites de certains suites d’entires. Proc London Math Soc 59, 417-438.
  • Fast H (1951). Sur la Convergence statistique. Colloq Math 2241-244.
  • Freedman AR, Sember JJ, Raphael M (1978). Some Cesaro type summability Spaces. Proc London Math Soc 37, 301-313.
  • Fridy JA (1985). On statistical convergence. Analysis 5, 301-313.
  • Fridy JA, Miller HI (1991). A matrix characterization of statistical convergence. Analysis 11, 59-66.
  • Kucukaslan M, Yılmazturk M (2012). Deferred statistical convergence. Kyungpook Math J (Submitted).
  • Maddox IJ (1967). Space of strongly summable functions. Oxford 2, Quart J Math 345-355.
  • Maddox IJ (1970). Elements of Functional Analysis, Cambridge at the University Press, 208 pp.
  • Mursaleen M (2000). λ-statistical convergence. Math Slavaca 50, 111-115.
  • Nuray F (2010). λ-strongly summable and statistical convergence, λ-statistical convergent functions. Int J Sci Tech 34, 335-338.
  • Steinhous H (1951). Sur la convergence ordinaire et la convergence asymtotique. Colloq Math 2, 73-74.
  • Schoenberg IJ (1959). The integrability of certain functions and related summability methods. Amer Math Monthly 66, 361-375.
  • Steinhaus H (1951). Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 273-74.
  • Osikiewicz JA (1997). Summability of Matrix submethods and spliced sequences. PhD. Thesis, August, 90 pp.
  • Zygmund A (1979). Trigonometric Series, Cambridge Univ Press, UK.

Yıl 2013, , 22 - 25, 23.06.2013

Mehmet Kucukaslan Mujde Yılmazturk

https://doi.org/10.17678/beuscitech.47136

Öz

Kaynakça

  • Agnew RP (1932). On deferred Cesaro Mean. Comm Ann Math, 33, 413-421.
  • Armitage DH, Maddox IJ (1989) A new type of Cesaro Mean. Analysis 9,195-204.
  • Buck RC (1953). Generalized asymptotic Density. Amer Math Comm 75, 335-346.
  • Connor JS (1988). The statistical and strong p-Cesaro of sequences. Analysis 847-63.
  • Connor JS (1989). On strong matrix summability with respect to a modulus and statistical convergence. Can Math Bull 32, 194-198.
  • Erdös P, Tenenbaum G (1989). Sur les densites de certains suites d’entires. Proc London Math Soc 59, 417-438.
  • Fast H (1951). Sur la Convergence statistique. Colloq Math 2241-244.
  • Freedman AR, Sember JJ, Raphael M (1978). Some Cesaro type summability Spaces. Proc London Math Soc 37, 301-313.
  • Fridy JA (1985). On statistical convergence. Analysis 5, 301-313.
  • Fridy JA, Miller HI (1991). A matrix characterization of statistical convergence. Analysis 11, 59-66.
  • Kucukaslan M, Yılmazturk M (2012). Deferred statistical convergence. Kyungpook Math J (Submitted).
  • Maddox IJ (1967). Space of strongly summable functions. Oxford 2, Quart J Math 345-355.
  • Maddox IJ (1970). Elements of Functional Analysis, Cambridge at the University Press, 208 pp.
  • Mursaleen M (2000). λ-statistical convergence. Math Slavaca 50, 111-115.
  • Nuray F (2010). λ-strongly summable and statistical convergence, λ-statistical convergent functions. Int J Sci Tech 34, 335-338.
  • Steinhous H (1951). Sur la convergence ordinaire et la convergence asymtotique. Colloq Math 2, 73-74.
  • Schoenberg IJ (1959). The integrability of certain functions and related summability methods. Amer Math Monthly 66, 361-375.
  • Steinhaus H (1951). Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 273-74.
  • Osikiewicz JA (1997). Summability of Matrix submethods and spliced sequences. PhD. Thesis, August, 90 pp.
  • Zygmund A (1979). Trigonometric Series, Cambridge Univ Press, UK.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Mehmet Kucukaslan Bu kişi benim

Mujde Yılmazturk Bu kişi benim

Yayımlanma Tarihi 23 Haziran 2013
Gönderilme Tarihi 8 Kasım 2012
Yayımlandığı Sayı Yıl 2013

Kaynak Göster

IEEE M. Kucukaslan ve M. Yılmazturk, “On strongly deferred Cesaro summability and deferred statistical convergence of the sequences”, Bitlis Eren University Journal of Science and Technology, c. 3, sy. 1, ss. 22–25, 2013, doi: 10.17678/beuscitech.47136.