Research Article

Properties of J_p-Statistical Convergence

Volume: 43 Number: 2 June 29, 2022
EN

Properties of J_p-Statistical Convergence

Abstract

In this study, different characterizations of J_p-statistically convergent sequences are given. The main features of J_p-statistically convergent sequences are investigated and the relationship between J_p-statistically convergent sequences and J_p-statistically Cauchy sequences is examined. The properties provided by the set of bounded and J_p statistical convergent sequences is shown. It is given that the statistical limit is unique. Furthermore, a sequence that J_p-statistical converges to the number L has a subsequence that converges to the same number of L, is shown. The analogs of J_p statistical convergent sequences is studied.

Keywords

Power series method, J_p-statistical convergence, J_p-statistical Cauchy

References

  1. [1] Zygmund A., Trigonometric Series. 3rd.ed. London: Cambridge Univ. Press, (2003),
  2. [2] Fast H., Sur la convergence statistique, Colloq. Math., 2 (1951) 241-244.
  3. [3] Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951) 73-74.
  4. [4] Buck R. C., Generalized asymptotic density, Amer. J. Math., 75 (2) (1953) 335-346.
  5. [5] Fridy, J. A., On statistical convergence, Analysis 5 (1985) 301-313.
  6. [6] Schoenberg I. J. , The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5) (1959) 361-375.
  7. [7] Connor J., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988) 47-63.
  8. [8] Connor J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32 (1989) 194-198.
  9. [9] Belen C., Mursaleen M.,Yildirim M., Statistical A-summability of double sequences and a Korovkin type approximation theorem, Bull. Korean Math. Soc., 49 (4) (2012) 851–861.
  10. [10] Belen C., Some Tauberian theorems for weighted means of bounded double sequences, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 63 (1) (2017) 115–122.
APA
Sümbül, C., Belen, C., & Yıldırım, M. (2022). Properties of J_p-Statistical Convergence. Cumhuriyet Science Journal, 43(2), 294-298. https://doi.org/10.17776/csj.1064559
AMA
1.Sümbül C, Belen C, Yıldırım M. Properties of J_p-Statistical Convergence. CSJ. 2022;43(2):294-298. doi:10.17776/csj.1064559
Chicago
Sümbül, Canan, Cemal Belen, and Mustafa Yıldırım. 2022. “Properties of J_p-Statistical Convergence”. Cumhuriyet Science Journal 43 (2): 294-98. https://doi.org/10.17776/csj.1064559.
EndNote
Sümbül C, Belen C, Yıldırım M (June 1, 2022) Properties of J_p-Statistical Convergence. Cumhuriyet Science Journal 43 2 294–298.
IEEE
[1]C. Sümbül, C. Belen, and M. Yıldırım, “Properties of J_p-Statistical Convergence”, CSJ, vol. 43, no. 2, pp. 294–298, June 2022, doi: 10.17776/csj.1064559.
ISNAD
Sümbül, Canan - Belen, Cemal - Yıldırım, Mustafa. “Properties of J_p-Statistical Convergence”. Cumhuriyet Science Journal 43/2 (June 1, 2022): 294-298. https://doi.org/10.17776/csj.1064559.
JAMA
1.Sümbül C, Belen C, Yıldırım M. Properties of J_p-Statistical Convergence. CSJ. 2022;43:294–298.
MLA
Sümbül, Canan, et al. “Properties of J_p-Statistical Convergence”. Cumhuriyet Science Journal, vol. 43, no. 2, June 2022, pp. 294-8, doi:10.17776/csj.1064559.
Vancouver
1.Canan Sümbül, Cemal Belen, Mustafa Yıldırım. Properties of J_p-Statistical Convergence. CSJ. 2022 Jun. 1;43(2):294-8. doi:10.17776/csj.1064559