Research Article
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Year 2024, , 83 - 93, 31.07.2024
https://doi.org/10.54974/fcmathsci.1357160

Abstract

References

  • Abazari R., Statistical convergence in g-metric spaces, Filomat, 36(5), 1461-1468, 2022.
  • 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.
  • Bilalov B., Nazarova T., On statistical convergence in metric spaces, Journal of Mathematics Research, 7(1), 37-43, 2015.
  • Burgin M., Duman O., Statistical convergence and convergence in statistics, arXiv:math/0612179, 2006.
  • Connor J.S., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8(1-2), 47-64, 1988.
  • 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.
  • Dhage B.G., Generalized metric spaces and mapping with fixed point, Bulletin of the Calcutta Mathematical Society, 84(4), 329-336, 1992.
  • Duman O., Khan M.K., Orhan C., A-Statistical convergence of approximating operators, Mathematical Inequalities & Applications, 6(4), 689-699, 2003.
  • Fast H., Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), 241-244, 1951.
  • Freedman A.R., Sember J.J., Densities and summability, Pacific Journal of Mathematics, 95(2), 293- 305, 1981.
  • Fréchet M.M., Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matematico di Palermo (1884-1940), 22(1), 1-72, 1906.
  • Fridy J.A., On statistical convergence, Analysis, 5, 301-313, 1985.
  • Fridy J.A., Khan M.K., Tauberian theorems via statistical convergence, Journal of Mathematical Analysis and Applications, 228(1), 73-95, 1998.
  • Gähler S., 2-metrische Räume und ihre topologische struktur, Mathematische Nachrichten, 26(1-4), 115-148, 1963.
  • Gürdal M., Pehlivan S., The statistical convergence in 2-Banach spaces, Thai Journal of Mathematics, 2(1), 107-113, 2004.
  • Kedian L., Shou L., Ying G., On statistical convergence in cone metric spaces, Topology and Its Applications, 196, 641-651, 2015.
  • Khamsi M.A., Generalized metric spaces: A survey, Journal of Fixed Point Theory and Applications, 17(3), 455-475, 2015.
  • Mustafa Z., Sims B., Some remarks concerning D-metric spaces, In International Conferences on Fixed Point Theory and Application, Valencia, Spain, 189-198, 2003.
  • Mustafa Z., Sims B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2), 289-297, 2006.
  • Nuray F., Statistical convergence in 2-metric spaces, Journal of Classical Analysis, 16(2), 115-123, 2020.
  • Nuray F., Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1), 155-160, 2022.
  • Reddy B.S., Statistical convergence in n-normed spaces, International Mathematical Forum, 24, 1185- 1193, 2010.
  • Savaş E., Das P., A generalized statistical convergence via ideals, Applied Mathematics Letters, 826- 830, 2010.
  • Schoenberg I.J., The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66, 361-375, 1959.
  • Sedghi S., Shobeand N., Aliouche A., A generalization of fixed point theorem in S -metric spaces, Matematički Vesnik, 64(3), 258-266, 2012.
  • Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum, 2(1), 73-74, 1951.
  • Zygmund A., Trigonometric Series, Cambridge University Press, 1979.

Statistical Convergence in A-Metric Spaces

Year 2024, , 83 - 93, 31.07.2024
https://doi.org/10.54974/fcmathsci.1357160

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.

References

  • Abazari R., Statistical convergence in g-metric spaces, Filomat, 36(5), 1461-1468, 2022.
  • 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.
  • Bilalov B., Nazarova T., On statistical convergence in metric spaces, Journal of Mathematics Research, 7(1), 37-43, 2015.
  • Burgin M., Duman O., Statistical convergence and convergence in statistics, arXiv:math/0612179, 2006.
  • Connor J.S., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8(1-2), 47-64, 1988.
  • 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.
  • Dhage B.G., Generalized metric spaces and mapping with fixed point, Bulletin of the Calcutta Mathematical Society, 84(4), 329-336, 1992.
  • Duman O., Khan M.K., Orhan C., A-Statistical convergence of approximating operators, Mathematical Inequalities & Applications, 6(4), 689-699, 2003.
  • Fast H., Sur la convergence statistique, Colloquium Mathematicae, 2(3-4), 241-244, 1951.
  • Freedman A.R., Sember J.J., Densities and summability, Pacific Journal of Mathematics, 95(2), 293- 305, 1981.
  • Fréchet M.M., Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matematico di Palermo (1884-1940), 22(1), 1-72, 1906.
  • Fridy J.A., On statistical convergence, Analysis, 5, 301-313, 1985.
  • Fridy J.A., Khan M.K., Tauberian theorems via statistical convergence, Journal of Mathematical Analysis and Applications, 228(1), 73-95, 1998.
  • Gähler S., 2-metrische Räume und ihre topologische struktur, Mathematische Nachrichten, 26(1-4), 115-148, 1963.
  • Gürdal M., Pehlivan S., The statistical convergence in 2-Banach spaces, Thai Journal of Mathematics, 2(1), 107-113, 2004.
  • Kedian L., Shou L., Ying G., On statistical convergence in cone metric spaces, Topology and Its Applications, 196, 641-651, 2015.
  • Khamsi M.A., Generalized metric spaces: A survey, Journal of Fixed Point Theory and Applications, 17(3), 455-475, 2015.
  • Mustafa Z., Sims B., Some remarks concerning D-metric spaces, In International Conferences on Fixed Point Theory and Application, Valencia, Spain, 189-198, 2003.
  • Mustafa Z., Sims B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2), 289-297, 2006.
  • Nuray F., Statistical convergence in 2-metric spaces, Journal of Classical Analysis, 16(2), 115-123, 2020.
  • Nuray F., Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1), 155-160, 2022.
  • Reddy B.S., Statistical convergence in n-normed spaces, International Mathematical Forum, 24, 1185- 1193, 2010.
  • Savaş E., Das P., A generalized statistical convergence via ideals, Applied Mathematics Letters, 826- 830, 2010.
  • Schoenberg I.J., The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66, 361-375, 1959.
  • Sedghi S., Shobeand N., Aliouche A., A generalization of fixed point theorem in S -metric spaces, Matematički Vesnik, 64(3), 258-266, 2012.
  • Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum, 2(1), 73-74, 1951.
  • Zygmund A., Trigonometric Series, Cambridge University Press, 1979.
There are 27 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Articles
Authors

Ramazan Sunar 0000-0001-8107-5618

Publication Date July 31, 2024
Published in Issue Year 2024

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.