Journals / Konuralp Journal of Mathematics / 2026 / Volume: 12 Issue: 1

Statistical Convergence of Matrix Sequences

Elif Nuray Yıldırım(İSTANBUL TİCARET ÜNİVERSİTESİ)0000-0002-2934-892X
Pages
—
Publication Date
2024-04-30
DOI
—
🏛️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)

This leads us to an initial analysis of the Tauberian conditions for the statistical convergence of matrix sequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper extends the statistical convergence of real or complex numbers to the real square matrices sequences .
📊
Key Findings & Data:In this context, we investigate the relation between the statistical convergence, statistical Cauchy condition, strong Cesaro summability of matrices sequences.
💡
Conclusion & Impact:This leads us to an initial analysis of the Tauberian conditions for the statistical convergence of matrix sequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:matrix sequence · statistical convergence · Cesaro summability

Abstract

This paper extends the statistical convergence of real or complex numbers to the real square matrices sequences . In this context, we investigate the relation between the statistical convergence, statistical Cauchy condition, strong Cesaro summability of matrices sequences. This leads us to an initial analysis of the Tauberian conditions for the statistical convergence of matrix sequences.

🔖

Cite This Article

Yıldırım, E. N. (2024). Statistical Convergence of Matrix Sequences. Konuralp Journal of Mathematics, Volume: 12 Issue: 1. https://ajindex.com/articles/1521505

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. M. Baronti, and P. Papini, Convergence of sequences of sets, Methods of functional analysis in approximation theory,76, Birkhauser-Verlag, Basel,(1986), 133–155.
  2. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc., 31, (1985), 421—432.
  3. G. Beer, Wijsman convergence: A survey, Set-Valued Var. Anal., 2, (1994), 77—94.
  4. J. Connor, The statistical and strong p-Ces`aro convergence of sequences, Analysis, 8 (1988) 46–63. [5] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241–244.
  5. J. A. Fridy, On statistical convergence, Analysis, 5 (1985,) 301–313.
  6. J.A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993), 497–504.
  7. J.A. Fridy, and M.K. Khan, Tauberian theorems via statistical convergence, J. Math. Anal. Appl., 228 (1998), 73–95.
  8. A.D. Gadjiev, and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. of Math., 32(1) (2002), 129–138.
  9. H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995), 1811–1819.
  10. F. Nuray and B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49, (2012), 87–99.
  11. F. Nuray, U. Ulusu and E. D¨undar, Ces`aro summability of double sequences of sets, Gen. Math. Notes 25(1), (2014), 8–18.
  12. S. Pehlivan and M. A. Mamedov, Statistical cluster points and turnpikes, Optimization, 48 (2000), 93–106.
  13. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150.
  14. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  15. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73–74.
  16. U. Ulusu and F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics, 4(2), (2012), 99–109.
  17. U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, Journal of Applied Mathematics and Bioinformatics, 33, (2013), 75–88.
  18. U. Ulusu and F. Nuray, Lacunary statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2), 176–184 (2015).
  19. U. Ulusu and F. Nuray, E. Dundar, I-limit and I-cluster points for functions defined on amenable semigroup, Fundamental Journal of Mathematics and Applications, 4(2), 45–48 (2021).
  20. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70, (1964), 186–188.
  21. R. A. Wijsman, Convergence of Sequences of Convex sets, Cones and Functions II, Trans. Amer. Math. Soc., 123(1), (1966), 32–45.
  22. A. Zygmund, Trigonometric series, 2nd ed,. Cambridge University Press, Cambridge, 1979.