Year 2019, Volume 1, Issue 1, Pages 40 - 47 2019-01-15

On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space

Çiğdem Bektaş [1] , Emine ÖZÇELİK [2]

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In this study, we introduce the concepts of strongly -Cesàro summability, -statistical Cauchy sequence and -statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them.


In this study, we introduce the concepts of strongly  ($\Delta ^{m}$,p)-Cesàro summability,  $\Delta ^{m}-statistical Cauchy sequence and  $\Delta ^{m}-statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them.

Statistical convergence, statistical Cauchy, paranormed space
  • 1. Fast, H., Sur la convergence statistique, Colloq. Math., 2, 241-244 (1951)
  • 2. Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2, 73-74 (1951)
  • 3. Fridy, J. A., On statistical convergence, Analysis, 5, 301-313 (1985)
  • 4. Šalát, T., On statisticaly convergent sequences of real numbers, Math Slovaca, 30, 139-150 (1980)
  • 5. Kolk, E., The Statistical convergence in Banach spaces, Tartu Ül. Toimetised, 928, 41-52 (1991)
  • 6. Alotaibi, A., Alroqi, M. A., Statistical convergence in a paranormed space, J. Inequal. Appl., 2012, 2012:39, 6 pp.
  • 7. Nakano, H., Concave modulars, J. Math. Soc. Japan 5(1953), 29-49.
  • 8. Mohammed, A., Mursaleen, M., λ-statistical convergence in paranormed space, Abstr. Appl. Anal. 2013, Art. ID 264520, 5 pp.
  • 9. Çolak, R., Bektaş, Ç. A., Altınok, H., Ercan, S., On inclusion relations between some sequence spaces, Int. J. Anal. 2016, Art. ID 7283527, 4 pp.
  • 10. Ercan, S., Altın, Y., Bektaş, Ç., On weak lambda-Statistical convergence of order alpha, U.P.B. Sci. Bull., Series A, 80(2), 215-226 (2018)
  • 11. Et, M., Çolak, R., On some generalized difference sequence spaces, Soochow Journal of Mathematics, 21(4) 377-386 (1995).
  • 12. Ercan, S., Bektaş, Ç., Some generalized difference sequence spaces of non absolute type, General Mahematics Notes, 27(2), 37-46 (2015).
  • 13. F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monograph, İstanbul-2012, ISBN: 978-1-60805-420-6.
  • 14. Ercan, S., Some Cesàro-type summability and statistical convergence of sequences generated by fractional difference operator, AKU J. Sci. Eng., 18 (2018) 011302 (125-130)
Primary Language en
Subjects Engineering
Journal Section Makaleler
Authors

Author: Çiğdem Bektaş (Primary Author)
Institution: FIRAT UNIVERSITY
Country: Turkey


Author: Emine ÖZÇELİK
Country: Turkey


Dates

Publication Date: January 15, 2019

Bibtex @research article { alku456415, journal = {ALKÜ Fen Bilimleri Dergisi}, issn = {}, eissn = {2667-7814}, address = {Alanya Alaaddin Keykubat University}, year = {2019}, volume = {1}, pages = {40 - 47}, doi = {}, title = {On Some Properties of \$\\Delta \^\{m\}\$-Statistical Convergence in a Paranormed Space}, key = {cite}, author = {Bektaş, Çiğdem and ÖZÇELİK, Emine} }
APA Bektaş, Ç , ÖZÇELİK, E . (2019). On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space. ALKÜ Fen Bilimleri Dergisi, 1 (1), 40-47. Retrieved from http://dergipark.org.tr/alku/issue/39176/456415
MLA Bektaş, Ç , ÖZÇELİK, E . "On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space". ALKÜ Fen Bilimleri Dergisi 1 (2019): 40-47 <http://dergipark.org.tr/alku/issue/39176/456415>
Chicago Bektaş, Ç , ÖZÇELİK, E . "On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space". ALKÜ Fen Bilimleri Dergisi 1 (2019): 40-47
RIS TY - JOUR T1 - On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space AU - Çiğdem Bektaş , Emine ÖZÇELİK Y1 - 2019 PY - 2019 N1 - DO - T2 - ALKÜ Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 40 EP - 47 VL - 1 IS - 1 SN - -2667-7814 M3 - UR - Y2 - 2018 ER -
EndNote %0 ALKÜ Fen Bilimleri Dergisi On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space %A Çiğdem Bektaş , Emine ÖZÇELİK %T On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space %D 2019 %J ALKÜ Fen Bilimleri Dergisi %P -2667-7814 %V 1 %N 1 %R %U
ISNAD Bektaş, Çiğdem , ÖZÇELİK, Emine . "On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space". ALKÜ Fen Bilimleri Dergisi 1 / 1 (January 2019): 40-47.
AMA Bektaş Ç , ÖZÇELİK E . On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space. ALKÜ Fen Bilimleri Dergisi. 2019; 1(1): 40-47.
Vancouver Bektaş Ç , ÖZÇELİK E . On Some Properties of $\Delta ^{m}$-Statistical Convergence in a Paranormed Space. ALKÜ Fen Bilimleri Dergisi. 2019; 1(1): 47-40.