Koray İbrahim Atabey, Muhammed Çınar

DOI Number
First page
Last page


In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{\Delta_{\beta}^{\tilde{\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ statistical Cauchy and p-strongly $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ Cesàro summability, $(0<p<\infty)$ for double sequences. We also give some inclusion relations between $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ statistical convergence and p-strongly $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ Cesàro summability $(0<p<\infty)$.


Statistical convergence, difference sequence, Cesàro summability

Full Text:



A. Aizpuru , M. C. Listan-Garcia, and F. Rambla-Barreno: Density by moduli and statistical convergence. Quaestiones Mathematicae 37.4 (2014), 525–530.

K. E. Akbas¸ and M. Isık: On asymptotically λ− statistical equivalent sequences of order α in probability. Filomat 34.13 (2020), 4359–4365.

K. I. Atabey and M. Cınar: On Statistical Convergence of Difference Double Sequence of Fractional Order. BEU J. Science 92 (2020), 615–628.

P. Baliarsingh: Some new difference sequence spaces of fractional order and their dual spaces. Appl. Math. Comput. 219.18 (2013), 189737—9742.

P. Baliarsingh: On difference double sequence spaces of fractional order. Indian J. Math 58.3 (2016), 287–310.

R. Colak and Y. Altin: Statistical convergence of double sequences of order α. Journal of function spaces and Applications (2013), Art. ID 682823, 5 pp

J.S. Connor: The statistical and strong p-Cesaro convergence of sequences. Analysis 8.1-2 (1988), 47–64.

S. Ercan: Some Cesaro-Type Summability and Statistical Convergence of Sequences Generated by Fractional Difference Operator. Afyon Kocatepe Universitesi Fen Ve Muhendislik Bilimleri Dergisi 18.1 (2018), 125–130.

M. Et and R. Colak: On generalized difference sequence spaces. Soochow J. Math. 21.4 (1995), 377–386.

H. Fast: Sur la convergence statistique. In Colloquium mathematicae. In Colloquium mathematicae 2 (1951), 241–244.

J.A. Fridy: On statistical convergence. Analysis 5.4 (1985), 301–314.

M. Gungor and M. Et: Δr−Strongly almost summable sequences defined by Orlicz functions. Indian Journal of Pure and Applied Mathematics 34.8 (2003), 1141–1152.

M. Gungor, M. Et and Y. Altın : Strongly (Vρ, λ, q)−summable sequences defined by Orlicz functions. Appl. Math. Comput.157.2 (2004), 561–571.

M. Isik and K. E. Akbas¸: On asymptotically λ− statistical convergence of order α in probability. J. Inequal. Spec. Funct 8.4 (2017), 57–64.

M. Isik and K. E. Akbas: On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability in probability. ITM Web of Conferences 13 (2017), 01024.

H. Kizmaz: On certain sequence spaces. Canadian Mathematical Bulletin 24.2 (1981), 169–176.

M. Mursaleen and O. H. H. Edely: Statistical convergence of double sequences. J. Math. Anal. Appl. 288.1 (2003), 223–231.

H. Nakano: Modulared sequence spaces. Proc. Japan Acad. 27 (1951), 508–512.

I. J. Schoenberg: The integrability of certain functions and related summability methods. The American mathematical monthly 66.5 (1959), 361–775.

H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique. In Colloq. Math. 2 (1951), 73–74.

B. Torgut and Y. Altin: f− Statistical Convergence of Double Sequences of Order α. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90 (2020), 803-–808.

A. Zygmund: Trigonometric Series. Cambridge University Press, Cambridge, UK, 1979.

DOI: https://doi.org/10.22190/FUMI211029044A


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)