Research Article
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Year 2024, Volume: 12 Issue: 1, 74 - 79, 30.04.2024

Abstract

References

  • [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.
  • [6] J. A. Fridy, On statistical convergence, Analysis, 5 (1985,) 301–313.
  • [7] J.A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993), 497–504.
  • [8] J.A. Fridy, and M.K. Khan, Tauberian theorems via statistical convergence, J. Math. Anal. Appl., 228 (1998), 73–95.
  • [9] A.D. Gadjiev, and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. of Math., 32(1) (2002), 129–138.
  • [10] H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995), 1811–1819.
  • [11] F. Nuray and B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49, (2012), 87–99.
  • [12] F. Nuray, U. Ulusu and E. D¨undar, Ces`aro summability of double sequences of sets, Gen. Math. Notes 25(1), (2014), 8–18.
  • [13] S. Pehlivan and M. A. Mamedov, Statistical cluster points and turnpikes, Optimization, 48 (2000), 93–106.
  • [14] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150.
  • [15] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [16] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73–74.
  • [17] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics, 4(2), (2012), 99–109.
  • [18] U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, Journal of Applied Mathematics and Bioinformatics, 33, (2013), 75–88.
  • [19] U. Ulusu and F. Nuray, Lacunary statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2), 176–184 (2015).
  • [20] 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).
  • [21] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70, (1964), 186–188.
  • [22] R. A. Wijsman, Convergence of Sequences of Convex sets, Cones and Functions II, Trans. Amer. Math. Soc., 123(1), (1966), 32–45.
  • [23] A. Zygmund, Trigonometric series, 2nd ed,. Cambridge University Press, Cambridge, 1979.

Statistical Convergence of Matrix Sequences

Year 2024, Volume: 12 Issue: 1, 74 - 79, 30.04.2024

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.

References

  • [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.
  • [6] J. A. Fridy, On statistical convergence, Analysis, 5 (1985,) 301–313.
  • [7] J.A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993), 497–504.
  • [8] J.A. Fridy, and M.K. Khan, Tauberian theorems via statistical convergence, J. Math. Anal. Appl., 228 (1998), 73–95.
  • [9] A.D. Gadjiev, and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. of Math., 32(1) (2002), 129–138.
  • [10] H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995), 1811–1819.
  • [11] F. Nuray and B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49, (2012), 87–99.
  • [12] F. Nuray, U. Ulusu and E. D¨undar, Ces`aro summability of double sequences of sets, Gen. Math. Notes 25(1), (2014), 8–18.
  • [13] S. Pehlivan and M. A. Mamedov, Statistical cluster points and turnpikes, Optimization, 48 (2000), 93–106.
  • [14] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150.
  • [15] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [16] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73–74.
  • [17] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics, 4(2), (2012), 99–109.
  • [18] U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, Journal of Applied Mathematics and Bioinformatics, 33, (2013), 75–88.
  • [19] U. Ulusu and F. Nuray, Lacunary statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2), 176–184 (2015).
  • [20] 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).
  • [21] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70, (1964), 186–188.
  • [22] R. A. Wijsman, Convergence of Sequences of Convex sets, Cones and Functions II, Trans. Amer. Math. Soc., 123(1), (1966), 32–45.
  • [23] A. Zygmund, Trigonometric series, 2nd ed,. Cambridge University Press, Cambridge, 1979.
There are 22 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Elif Nuray Yıldırım 0000-0002-2934-892X

Early Pub Date April 29, 2024
Publication Date April 30, 2024
Submission Date March 12, 2024
Acceptance Date April 16, 2024
Published in Issue Year 2024 Volume: 12 Issue: 1

Cite

APA Nuray Yıldırım, E. (2024). Statistical Convergence of Matrix Sequences. Konuralp Journal of Mathematics, 12(1), 74-79.
AMA Nuray Yıldırım E. Statistical Convergence of Matrix Sequences. Konuralp J. Math. April 2024;12(1):74-79.
Chicago Nuray Yıldırım, Elif. “Statistical Convergence of Matrix Sequences”. Konuralp Journal of Mathematics 12, no. 1 (April 2024): 74-79.
EndNote Nuray Yıldırım E (April 1, 2024) Statistical Convergence of Matrix Sequences. Konuralp Journal of Mathematics 12 1 74–79.
IEEE E. Nuray Yıldırım, “Statistical Convergence of Matrix Sequences”, Konuralp J. Math., vol. 12, no. 1, pp. 74–79, 2024.
ISNAD Nuray Yıldırım, Elif. “Statistical Convergence of Matrix Sequences”. Konuralp Journal of Mathematics 12/1 (April 2024), 74-79.
JAMA Nuray Yıldırım E. Statistical Convergence of Matrix Sequences. Konuralp J. Math. 2024;12:74–79.
MLA Nuray Yıldırım, Elif. “Statistical Convergence of Matrix Sequences”. Konuralp Journal of Mathematics, vol. 12, no. 1, 2024, pp. 74-79.
Vancouver Nuray Yıldırım E. Statistical Convergence of Matrix Sequences. Konuralp J. Math. 2024;12(1):74-9.
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