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Statistical Convergence on b-Metric Spaces

Year 2025, Volume: 17 Issue: 1, 275 - 281, 30.06.2025
https://doi.org/10.47000/tjmcs.1708269

Abstract

This paper investigates the idea of statistical convergence in the context of $b$-metric spaces. As a generalization of classical metric spaces, $b$-metric spaces offer a useful structure to examine  the basic concepts of statistical convergence. The results indicate that b-metric spaces provide an impressive theoretical basis for both convergence theory and fixed point analysis.

References

  • Abazaria, R., Statistical Convergence in-Metric Spaces, Filomat, 36(5) (2022), 1461-1468.
  • Bakhtin, I.A. , The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst., 30(1989), 26-37.
  • Bilalov, B., Nazarova, T., On statistical convergence in metric spaces , Journal of Mathematics Research, 7(1) (2015), 37.
  • Czerwik, S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
  • Fast, H. , Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
  • Fridy, J. A., On Statistical Convergence, Analysis, 5(1985), 301-313.
  • İlkhan, M. and Kara, E. E., On statistical convergence in quasi-metric spaces , Demonstratio Mathematica, 52(1) (2019), 225-236.
  • Karapınar, E., A Short Survey on the Recent Fixed Point Results on b-Metric Spaces, Constructive Mathematical Analysis, 1(1) (2018), 15-44.
  • Li, K., Lin, S., and Ge, Y., On statistical convergence in cone metric spaces, Topology and its Applications, 196 (2015), 641-651.
  • Niven, I., Zuckerman, H.S. and Montgomery, H.L. , An Introduction to the Theory of Numbers (fifth edition), John Wiley & Sons, Inc., New York, 1991.
  • Nuray, F. Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1) (2022), 155-160.
  • Sunar, R. Statistical convergence in A-metric spaces, Fundamentals of Contemporary Mathematical Sciences, 5(2) (2024), 83-93.

Year 2025, Volume: 17 Issue: 1, 275 - 281, 30.06.2025
https://doi.org/10.47000/tjmcs.1708269

Abstract

References

  • Abazaria, R., Statistical Convergence in-Metric Spaces, Filomat, 36(5) (2022), 1461-1468.
  • Bakhtin, I.A. , The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst., 30(1989), 26-37.
  • Bilalov, B., Nazarova, T., On statistical convergence in metric spaces , Journal of Mathematics Research, 7(1) (2015), 37.
  • Czerwik, S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
  • Fast, H. , Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
  • Fridy, J. A., On Statistical Convergence, Analysis, 5(1985), 301-313.
  • İlkhan, M. and Kara, E. E., On statistical convergence in quasi-metric spaces , Demonstratio Mathematica, 52(1) (2019), 225-236.
  • Karapınar, E., A Short Survey on the Recent Fixed Point Results on b-Metric Spaces, Constructive Mathematical Analysis, 1(1) (2018), 15-44.
  • Li, K., Lin, S., and Ge, Y., On statistical convergence in cone metric spaces, Topology and its Applications, 196 (2015), 641-651.
  • Niven, I., Zuckerman, H.S. and Montgomery, H.L. , An Introduction to the Theory of Numbers (fifth edition), John Wiley & Sons, Inc., New York, 1991.
  • Nuray, F. Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1) (2022), 155-160.
  • Sunar, R. Statistical convergence in A-metric spaces, Fundamentals of Contemporary Mathematical Sciences, 5(2) (2024), 83-93.
There are 12 citations in total.

Details

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

Ceylan Yalçın 0000-0003-0989-6280

Submission Date May 28, 2025
Acceptance Date June 24, 2025
Publication Date June 30, 2025
Published in Issue Year 2025 Volume: 17 Issue: 1

Cite

APA Yalçın, C. (2025). Statistical Convergence on b-Metric Spaces. Turkish Journal of Mathematics and Computer Science, 17(1), 275-281. https://doi.org/10.47000/tjmcs.1708269
AMA 1.Yalçın C. Statistical Convergence on b-Metric Spaces. TJMCS. 2025;17(1):275-281. doi:10.47000/tjmcs.1708269
Chicago Yalçın, Ceylan. 2025. “Statistical Convergence on B-Metric Spaces”. Turkish Journal of Mathematics and Computer Science 17 (1): 275-81. https://doi.org/10.47000/tjmcs.1708269.
EndNote Yalçın C (June 1, 2025) Statistical Convergence on b-Metric Spaces. Turkish Journal of Mathematics and Computer Science 17 1 275–281.
IEEE [1]C. Yalçın, “Statistical Convergence on b-Metric Spaces”, TJMCS, vol. 17, no. 1, pp. 275–281, June 2025, doi: 10.47000/tjmcs.1708269.
ISNAD Yalçın, Ceylan. “Statistical Convergence on B-Metric Spaces”. Turkish Journal of Mathematics and Computer Science 17/1 (June 1, 2025): 275-281. https://doi.org/10.47000/tjmcs.1708269.
JAMA 1.Yalçın C. Statistical Convergence on b-Metric Spaces. TJMCS. 2025;17:275–281.
MLA Yalçın, Ceylan. “Statistical Convergence on B-Metric Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 1, June 2025, pp. 275-81, doi:10.47000/tjmcs.1708269.
Vancouver 1.Yalçın C. Statistical Convergence on b-Metric Spaces. TJMCS [Internet]. 2025 June 1;17(1):275-81. Available from: https://izlik.org/JA76AK87PR