SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 70 Issue: 1

Statistical extension of bounded sequence space

Maya Altınok(Tarsus Üniversitesi)0000-0002-6671-743X
Mehmet Küçükaslan(MERSİN ÜNİVERSİTESİ)0000-0002-3183-3123
Umutcan Kaya(MERSİN ÜNİVERSİTESİ)0000-0002-0419-6106
Pages
—
Publication Date
2021-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, it is shown that the space $l_{\infty}$ is a non-porous subset of $l_{\infty}^{st}$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper by using natural density real valued bounded sequence space $l_{\infty}$ is extented and statistical bounded sequence space $l_{\infty}^{st}$ is obtained.
📊
Key Findings & Data:Besides the main properties of the space $l_{\infty}^{st}$, it is shown that $l_{\infty}^{st}$ is a Banach space with a norm produced with the help of density.
💡
Conclusion & Impact:Finally, it is shown that the space $l_{\infty}$ is a non-porous subset of $l_{\infty}^{st}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Natural density · statistical convergence · statistical sup norm

Abstract

In this paper by using natural density real valued bounded sequence space $l_{\infty}$ is extented and statistical bounded sequence space $l_{\infty}^{st}$ is obtained. Besides the main properties of the space $l_{\infty}^{st}$, it is shown that $l_{\infty}^{st}$ is a Banach space with a norm produced with the help of density. Also, it is shown that there is no matrix extension of the space $l_{\infty}$ that its bounded sequences space covers $l_{\infty}^{st}$. Finally, it is shown that the space $l_{\infty}$ is a non-porous subset of $l_{\infty}^{st}$.

🔖

Cite This Article

Altınok, M., Küçükaslan, M., Kaya, U. (2021). Statistical extension of bounded sequence space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 70 Issue: 1. https://doi.org/10.31801/cfsuasmas.736132

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (25)

  1. Altınok, M., Küçükaslan, M., A-statistical convergence and A-statistical monotonicity, Applied Mathematics E-Notes, 13 (2013), 249-260.
  2. Altınok, M., Küçükaslan, M., Ideal limit superior-inferior, Gazi University Journal of Science, 30 (1) (2017), 401-411.
  3. Altınok, M., Küçükaslan, M., A-statistical supremum-infimum and A-statistical convergence, Azerbaijan Journal of Mathematics, 4 (2) (2014), 31-42.
  4. Altınok, M., Porosity supremum-infimum and porosity convergence, Konuralp Journal of Mathematics, 6 (1) (2018), 163-170.
  5. Bilalov, B., Nazarova, T., On statistical convergence in metric spaces, Journal of Mathematics Research, 7 (1) (2015), 37-43.
  6. Bilalov, B., Nazarova, T., On statistical type convergence in uniform spaces, Bull. of the Iranian Math. Soc., 42 (4) (2016), 975-986.
  7. Cabrera, M. O., Rosalsky, A., Ünver, M., Volodin, A., On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense, TEST, (2020).
  8. Et, M., Sengül, H., Some Cesaro type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28 (8) (2014), 1593-1602.
  9. Erdös, P., Tenenboum, G., Sur les densities de certaines suites dentiers, Proc. London Math. Soc., 59 (1989), 417-438.
  10. Fast, H., Sur la convergence statistique, Colloquium Mathematicae, 2 (3-4) (1951), 241-244.
  11. Fridy, J. A., On statistical convergence, Analysis, 5 (1985), 301-313.
  12. Fridy, J. A., Khan, M. K., Tauberian theorems via statistical convergnece, J.Math. Anal.Appl., 228 (1998), 73-95.
  13. Gadjiev, A. D., Orhan, C., Some approximation theorems via statistical convergnece, Rocky Mountain J. Math., 32 (2002), 129-138.
  14. Kaya, E, Küçükaslan, M., Wagner, R., On statistical convergence and statistical monotonicity, Annales Univ. Sci. Budapest. Sect. Comp., 39 (2013), 257-270.
  15. Küçükaslan, M., Altınok, M., Statistical supremum-infimum and statistical convergence, The Aligarh Bulletin of Mathematics, 32 (1-2) (2013), 1-16.
  16. Küçükaslan, M., Deger U., Dovgoshey O., On the Statistical Convergence of Metric-Valued Sequences, Ukrainian Mathematical Journal, 66 (5) (2014), 712-720.
  17. Lindenstrauss, J., Preiss, D., Tišer, J., Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces, Princeton University Press, 41 William Street, Princeton, New Jersey, 2012.
  18. Lonetti, P., Limit points of subsequences, Topology and its Applications, 263 (2019), 221-229.
  19. Miller, H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995), 1881-1919.
  20. Pratulananda, D., Savas, E., On Generalized Statistical and Ideal Convergence of Metric-Valued Sequences, Ukrainian Mathematical Journal, 68 (1) (2017), 1849-1859.
  21. Salat, T., On statistical convergent sequences of real numbers, Math. Slovaca, 30 (2) (1980), 139-150.
  22. Sanjoy Ghosal, K., Statistical convergence of a sequence of random variables and limits theorems, Applications of Mathematics, 58 (4) (2013), 423-437.
  23. Sandeep G., Bhardwaj V.K., On deferred f-statistical convergnece, Kyunpook Math.J., 58 (2018), 91-103.
  24. Steinhaus, H., Sur la convergene ordinaire et la convergence asymptotique, Colloquium Mathematicae, 2 (3-4) (1951), 73-74.
  25. Zygmund, A., Trigonometric series, vol II, Cambiridge Univ Press, 1979.