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Year 2025, Volume: 13 Issue: 2, 106 - 115, 26.06.2025

Prasenjit Bal , Bikram Sutradhar , Gourab Pal

https://doi.org/10.36753/mathenot.1675353

Abstract

References

  • [1] Yildirim, E. N.: Statistical convergence of matrix sequences. Konuralp Journal of Mathematics. 12(1), 74-79 (2024).
  • [2] Fast, H.: Sur la convergence statistique. Colloquium Mathematicum. 2, 241-244 (1951).
  • [3] Schoenberg, I. J.: The integrability of certain functions and related summability methods. American Mathematical Monthly. 66, 361-375 (1959).
  • [4] Datta, T., Bal, P., Rakshit, D.: Restricting statistical-star-γ covers up-to order α (0 < α < 1). Journal of the Indian Mathematical Society. 92(2), 320–328 (2025).
  • [5] Bal, P., Rakshit, D., Sarkar, S.: On star statistical compactness. Afrika Matematika. 36(1), 1-7 (2025).
  • [6] Bal, P., Das, P.: Bi statistical γ-covers controled by a pair of weight functions in topology. Pan-American Journal of Mathematics. 4 (3), 7 pages (2025).
  • [7] Das, P., Bal, P.: Statistical convergence restricted by weight functions and its application in the variation of γ-covers. Rendiconti dell’Istituto di Matematica dell’Università di Trieste. 56 (11), 13 pages (2024).
  • [8] Fridy, J. A.: On statistical convergence. Analysis. 5, 301-313 (1985).
  • [9] Salát, T.: On statistically convergent sequences of real numbers. Mathematica Slovaca. 30, 139-150 (1980).
  • [10] Connor, J.: The statistical and strong p-Cesàro convergence of sequences. Analysis. 8, 46-63 (1988).
  • [11] Das, P., Sarkar, S., Bal, P.: Statistical convergence in topological space controlled by modulus function. Ural Mathematical Journal. 10(2), 49–59 (2024).
  • [12] Yalvaç, ¸S.: Lacunary invariant statistical convergence in fuzzy normed spaces. Universal Journal of Mathematics and Applications. 7(2), 76-82 (2024).
  • [13] Gadjiev, A. D., Orhan C.: Some approximation theorems via statistical convergence. Rocky Mountain Journal of Mathematics. 32(1), 129-138 (2002).
  • [14] Engelking, R.: General topology. Sigma Series in Pure Mathematics. 6, (1989).
  • [15] Steinhaus, H.: Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum. 2, 73-74 (1951).
  • [16] Miller, H. I.: A measure theoretical subsequence characterization of statistical convergence. Transactions of the American Mathematical Society. 347, 1811-1819 (1995).
  • [17] Pehlivan, S., Mamedov, M. A.: Statistical cluster points and turnpiker. Optimization. 48, 93-106 (2000).

Statistical Convergence of Matrix Sequences and Eigenvalue Influences

Year 2025, Volume: 13 Issue: 2, 106 - 115, 26.06.2025

Prasenjit Bal , Bikram Sutradhar , Gourab Pal

https://doi.org/10.36753/mathenot.1675353

Abstract

This paper delves into the statistical convergence of sequences of square matrices with entries in the real or complex domain. Matrix sequence convergence is traditionally examined through two distinct lenses: element-wise convergence and norm convergence. We explore both paradigms, unraveling their interconnections through illustrative examples. Furthermore, we shed light on the intrinsic nature of matrix sequence convergence, emphasizing its intricate dependence on the eigenvalues of the matrices involved.

Keywords

Matrix sequence Statistical convergence eigenvalue

References

  • [1] Yildirim, E. N.: Statistical convergence of matrix sequences. Konuralp Journal of Mathematics. 12(1), 74-79 (2024).
  • [2] Fast, H.: Sur la convergence statistique. Colloquium Mathematicum. 2, 241-244 (1951).
  • [3] Schoenberg, I. J.: The integrability of certain functions and related summability methods. American Mathematical Monthly. 66, 361-375 (1959).
  • [4] Datta, T., Bal, P., Rakshit, D.: Restricting statistical-star-γ covers up-to order α (0 < α < 1). Journal of the Indian Mathematical Society. 92(2), 320–328 (2025).
  • [5] Bal, P., Rakshit, D., Sarkar, S.: On star statistical compactness. Afrika Matematika. 36(1), 1-7 (2025).
  • [6] Bal, P., Das, P.: Bi statistical γ-covers controled by a pair of weight functions in topology. Pan-American Journal of Mathematics. 4 (3), 7 pages (2025).
  • [7] Das, P., Bal, P.: Statistical convergence restricted by weight functions and its application in the variation of γ-covers. Rendiconti dell’Istituto di Matematica dell’Università di Trieste. 56 (11), 13 pages (2024).
  • [8] Fridy, J. A.: On statistical convergence. Analysis. 5, 301-313 (1985).
  • [9] Salát, T.: On statistically convergent sequences of real numbers. Mathematica Slovaca. 30, 139-150 (1980).
  • [10] Connor, J.: The statistical and strong p-Cesàro convergence of sequences. Analysis. 8, 46-63 (1988).
  • [11] Das, P., Sarkar, S., Bal, P.: Statistical convergence in topological space controlled by modulus function. Ural Mathematical Journal. 10(2), 49–59 (2024).
  • [12] Yalvaç, ¸S.: Lacunary invariant statistical convergence in fuzzy normed spaces. Universal Journal of Mathematics and Applications. 7(2), 76-82 (2024).
  • [13] Gadjiev, A. D., Orhan C.: Some approximation theorems via statistical convergence. Rocky Mountain Journal of Mathematics. 32(1), 129-138 (2002).
  • [14] Engelking, R.: General topology. Sigma Series in Pure Mathematics. 6, (1989).
  • [15] Steinhaus, H.: Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum. 2, 73-74 (1951).
  • [16] Miller, H. I.: A measure theoretical subsequence characterization of statistical convergence. Transactions of the American Mathematical Society. 347, 1811-1819 (1995).
  • [17] Pehlivan, S., Mamedov, M. A.: Statistical cluster points and turnpiker. Optimization. 48, 93-106 (2000).
There are 17 citations in total.

Details

Primary Language English
Subjects Approximation Theory and Asymptotic Methods
Journal Section Articles
Authors

Prasenjit Bal 0000-0001-5047-7390

Bikram Sutradhar 0009-0005-7277-822X

Gourab Pal 0009-0008-7148-7940

Early Pub Date June 21, 2025
Publication Date June 26, 2025
Submission Date April 13, 2025
Acceptance Date June 15, 2025
Published in Issue Year 2025 Volume: 13 Issue: 2

Cite

APA Bal, P., Sutradhar, B., & Pal, G. (2025). Statistical Convergence of Matrix Sequences and Eigenvalue Influences. Mathematical Sciences and Applications E-Notes, 13(2), 106-115. https://doi.org/10.36753/mathenot.1675353
AMA Bal P, Sutradhar B, Pal G. Statistical Convergence of Matrix Sequences and Eigenvalue Influences. Math. Sci. Appl. E-Notes. June 2025;13(2):106-115. doi:10.36753/mathenot.1675353
Chicago Bal, Prasenjit, Bikram Sutradhar, and Gourab Pal. “Statistical Convergence of Matrix Sequences and Eigenvalue Influences”. Mathematical Sciences and Applications E-Notes 13, no. 2 (June 2025): 106-15. https://doi.org/10.36753/mathenot.1675353.
EndNote Bal P, Sutradhar B, Pal G (June 1, 2025) Statistical Convergence of Matrix Sequences and Eigenvalue Influences. Mathematical Sciences and Applications E-Notes 13 2 106–115.
IEEE P. Bal, B. Sutradhar, and G. Pal, “Statistical Convergence of Matrix Sequences and Eigenvalue Influences”, Math. Sci. Appl. E-Notes, vol. 13, no. 2, pp. 106–115, 2025, doi: 10.36753/mathenot.1675353.
ISNAD Bal, Prasenjit et al. “Statistical Convergence of Matrix Sequences and Eigenvalue Influences”. Mathematical Sciences and Applications E-Notes 13/2 (June 2025), 106-115. https://doi.org/10.36753/mathenot.1675353.
JAMA Bal P, Sutradhar B, Pal G. Statistical Convergence of Matrix Sequences and Eigenvalue Influences. Math. Sci. Appl. E-Notes. 2025;13:106–115.
MLA Bal, Prasenjit et al. “Statistical Convergence of Matrix Sequences and Eigenvalue Influences”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 2, 2025, pp. 106-15, doi:10.36753/mathenot.1675353.
Vancouver Bal P, Sutradhar B, Pal G. Statistical Convergence of Matrix Sequences and Eigenvalue Influences. Math. Sci. Appl. E-Notes. 2025;13(2):106-15.
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