Statistical Convergence in A-Metric Spaces

Abstract

In this paper, we will present the notion of statistical convergence in A-metric spaces, which is an important concept in summability theory. We will define statistical convergence in A-metric spaces and investigate its basic properties. Furthermore, we will explore the relationship between strongly p-Cesàro and statistical convergence in A-metric spaces.

Keywords

• Statistical convergence
• Cauchy sequence
• A-metric spaces

References

1. Abazari R., Statistical convergence in g-metric spaces, Filomat, 36(5), 1461-1468, 2022.
2. Abbas M., Ali B., Suleiman Y.I., Generalized coupled common fixed point results in partially ordered A-metric spaces, Fixed Point Theory and Applications, 2015(1), 1-24, 2015.
3. Bilalov B., Nazarova T., On statistical convergence in metric spaces, Journal of Mathematics Research, 7(1), 37-43, 2015.
4. Burgin M., Duman O., Statistical convergence and convergence in statistics, arXiv:math/0612179, 2006.
5. Connor J.S., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8(1-2), 47-64, 1988.
6. Connor J., Ganichev M., Kadets V., A characterization of Banach spaces with separable duals via weak statistical convergence, Journal of Mathematical Analysis and Applications, 244, 251-261, 2000.
7. Dhage B.G., Generalized metric spaces and mapping with fixed point, Bulletin of the Calcutta Mathematical Society, 84(4), 329-336, 1992.
8. Duman O., Khan M.K., Orhan C., A-Statistical convergence of approximating operators, Mathematical Inequalities & Applications, 6(4), 689-699, 2003.

9. Fast H., Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), 241-244, 1951.
10. Freedman A.R., Sember J.J., Densities and summability, Pacific Journal of Mathematics, 95(2), 293- 305, 1981.
11. Fréchet M.M., Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matematico di Palermo (1884-1940), 22(1), 1-72, 1906.
12. Fridy J.A., On statistical convergence, Analysis, 5, 301-313, 1985.
13. Fridy J.A., Khan M.K., Tauberian theorems via statistical convergence, Journal of Mathematical Analysis and Applications, 228(1), 73-95, 1998.
14. Gähler S., 2-metrische Räume und ihre topologische struktur, Mathematische Nachrichten, 26(1-4), 115-148, 1963.
15. Gürdal M., Pehlivan S., The statistical convergence in 2-Banach spaces, Thai Journal of Mathematics, 2(1), 107-113, 2004.
16. Kedian L., Shou L., Ying G., On statistical convergence in cone metric spaces, Topology and Its Applications, 196, 641-651, 2015.
17. Khamsi M.A., Generalized metric spaces: A survey, Journal of Fixed Point Theory and Applications, 17(3), 455-475, 2015.
18. Mustafa Z., Sims B., Some remarks concerning D-metric spaces, In International Conferences on Fixed Point Theory and Application, Valencia, Spain, 189-198, 2003.
19. Mustafa Z., Sims B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2), 289-297, 2006.
20. Nuray F., Statistical convergence in 2-metric spaces, Journal of Classical Analysis, 16(2), 115-123, 2020.
21. Nuray F., Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1), 155-160, 2022.
22. Reddy B.S., Statistical convergence in n-normed spaces, International Mathematical Forum, 24, 1185- 1193, 2010.
23. Savaş E., Das P., A generalized statistical convergence via ideals, Applied Mathematics Letters, 826- 830, 2010.
24. Schoenberg I.J., The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66, 361-375, 1959.
25. Sedghi S., Shobeand N., Aliouche A., A generalization of fixed point theorem in S -metric spaces, Matematički Vesnik, 64(3), 258-266, 2012.
26. Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum, 2(1), 73-74, 1951.
27. Zygmund A., Trigonometric Series, Cambridge University Press, 1979.