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Dergiler / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 15 Issue: 2

Strongly Statistical Convergence of Order \alpha in Metric Spaces

Nazlım Deniz Aral(BİTLİS EREN ÜNİVERSİTESİ)0000-0002-8984-2620
Sayfa
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Yayın Tarihi
2026-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we introduce M-strongly statistical bounded sequences of order α in metric spaces.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper introduces the concepts of M-strongly statistical convergence and [M]_d^α-summability of order α in metric spaces (X,d), where M denotes a non-negative infinite matrix.
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Temel Bulgular & Veri:The relationship between these newly defined notions and M-strong convergence is examined in detail.
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Sonuç & Katkı:Finally, we introduce M-strongly statistical bounded sequences of order α in metric spaces.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:statistical convergence · strong convergence · infinite matrix

Abstract

This paper introduces the concepts of M-strongly statistical convergence and [M]_d^α-summability of order α in metric spaces (X,d), where M denotes a non-negative infinite matrix. The relationship between these newly defined notions and M-strong convergence is examined in detail. Conditions ensuring the uniqueness of limits for M-strongly statistically convergent sequences are established. Also, we propose the definition of M-strongly statistical Cauchy sequences of order α and study their connection to M-strongly statistical convergence. Finally, we introduce M-strongly statistical bounded sequences of order α in metric spaces.

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Bu Makaleye Atıf Yap

Aral, N. D. (2026). Strongly Statistical Convergence of Order \alpha in Metric Spaces. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 15 Issue: 2. https://doi.org/10.17798/bitlisfen.1806899

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Kaynakça (33)

  1. N. D. Aral, H. S. Kandemir and M. Et, “Deferred d-Statistical Boundedness of Order α in Metric Spaces,” Dera Natung Government College Research Journal, vol. 9, no. 1, pp. 1–12, 2024.
  2. B. Bilalov and T. Nazarova, “On statistical convergence in metric space,” Journal of Mathematics Research, vol. 7, pp. 37–43, 2015.
  3. R. Çolak, “Statistical convergence of order α,” in Modern Methods in Analysis and Its Applications, Anamaya Pub., New Delhi, India, pp. 121–129, 2010.
  4. J. S. Connor, “The statistical and strong p-Cesaro convergence of sequences,” Analysis, vol. 8, pp. 47–63, 1988.
  5. H. Çakallı and E. Savaş, “Statistical convergence of double sequences in topological group,” J. Comput. Anal. Appl., vol. 12, pp. 421–426, 2010.
  6. P. Das, S. Ghosal and S. Som, “Statistical convergence of order α in probability,” Arab J. Math. Sci., vol. 21, no. 2, pp. 253–265, 2015.
  7. O. Duman and C. Orhan, “μ-statistically convergent function sequences,” Czechoslovak Math. J., vol. 54, pp. 413–422, 2004.
  8. O. H. H. Edely, S. A. Mohiuddine and A. K. Noman, “Korovkin type approximation theorems obtained through generalized statistical convergence,” Appl. Math. Lett., vol. 23, pp. 1382–1387, 2010.
  9. P. Erdös and G. Tenenbaum, “Sur les densités de certaines soites d’entires,” Proceeding of the London Math. Socaity, vol. 59, no. 3, pp. 417–438, 1989.
  10. M. Et, H. Altınok and R. Çolak, “On λ-statistical convergence of difference sequences of fuzzy numbers,” Inform. Sci., vol. 176, pp. 2268–2278, 2006.
  11. M. Et, M. Çınar, H. Şengül Kandemir, “Deferred statistical convergence of order α in metric spaces,” AIMS Mathematics, vol. 5, no. 4, pp. 3731–3740, 2020.
  12. H. Fast, “Sur la convergence statistique,” Colloq. Math., vol. 2, pp. 241–244, 1951.
  13. A. R. Freedman and J. J. Sember, “Density and summability,” Pacific J. Math., vol. 95, no. 2, pp. 293–305, 1981.
  14. J. A. Fridy, “On statistical convergence,” Analysis (Berlin), vol. 5, no. 4, pp. 301–313, 1985.
  15. S. Ghosal, “Weighted statistical convergence of order α and its applications,” J. Egyptian Math. Soc., vol. 24, pp. 60–67, 2016.
  16. H. J. Hamilton, J. D. Hill, “On strong summability,” Am. J. Math., vol. 60, no. 3, pp. 588–594, 1938.
  17. V. Karakaya and T. A. Chishti, “Weighted statistical convergence,” Iran J. Sci. Technol. Trans. A Sci., vol. 33, no. 3, pp. 219–223, 2009.
  18. U. Kaya and N. D. Aral, “Strongly Statistical Convergence,” Ukr. Math. J., vol. 72, no. 2, pp. 246–259, 2020.
  19. İ. Kaya, Metrik Uzaylarda A-güçlü İstatistiksel Yakınsaklık, Bitlis Eren University Graduate School of Natural and Applied Sciences, Master Thesis, 2017.
  20. E. Kayan, R. Çolak and Y. Altın, “d-statistical convergence of order α and d-statistical boundedness of order α in metric spaces,” U.P.B. Sci. Bull., Series A, vol. 180, no. 4, pp. 229–238, 2018.
  21. Ö. Kişi, S. Çetin, and M. Gürdal, “Deferred Statistical Convergence of Sequences in Octonion-valued Metric Spaces,” Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 3, pp. 375–394, Apr. 2025.
  22. M. Küçükaslan, U. Değer and O. Dovgoshey, “On statistical convergence of Metric-Valued Sequences,” Ukr. Math. J., vol. 66, no. 5, pp. 712–720, 2014.
  23. H. I. Miller, “A measure theoretical subsequence characterization of statistical convergence,” Trans. Amer. Math. Soc., vol. 447, no. 5, pp. 1811–1819, 1995.
  24. M. Mursaleen, “λ-statistical convergence,” Math. Slovaca, vol. 50, pp. 111–115, 2000.
  25. M. Mursaleen, C. Çakan, S. A. Mohiuddine and E. Savaş, “Generalized statistical convergence and statistical core of double sequences,” Acta Math. Sin. (Engl. Ser.), vol. 26, pp. 2131–2144, 2010.
  26. M. Mursaleen and O. H. H. Edely, “Statistical convergence of double sequences,” J. Math. Anal. Appl., vol. 288, pp. 223–233, 2003.
  27. M. Mursaleen, V. Karakaya, M. Ertürk and F. Gürsoy, “Weighted statistical convergence and its application to Korovkin type approximation theorem,” Appl. Math. Comput., vol. 218, pp. 9132–9137, 2012.
  28. T. Salat, “On statistically convergent sequences of real numbers,” Mat. Slovaca, vol. 30, pp. 139–150, 1980.
  29. I. J. Schoenberg, “The Integrability of certain functions and related summability methods,” Amer. Math. Monthly, vol. 66, pp. 361–375, 1959.
  30. H. Steinhaus, “Sur la convergence ordinaire et la convergence asymptotique,” Colloq. Math., vol. 2, pp. 71–74, 1951.
  31. H. Şengül and M. Et, “On lacunary statistical convergence of order α,” Acta Math. Sci., vol. 2, no. 34, pp. 473–482, 2014.
  32. H. Şengül, M. Et and H. Çakallı, “Lacunary d statistical convergence and lacunary d statistical boundedness in metric spaces,” AIP Conference Proceedings.
  33. A. Zygmund, Trigonometric Series. Cambridge University Press, Cambridge, UK, 1979.