Some Results For Probabilistic Generalized Metric Spaces


Abstract views: 16 / PDF downloads: 12

Authors

  • Ömer Kişi Bartın University
  • Mehmet Gürdal Suleyman Demirel University
  • Elif Hevesker Bartın University

Keywords:

Probabilistic Generalized Metric Space, -Statistical Convergence, �-Statistical Cauchyness.

Abstract

In this research, we examine some fundamental characteristics of -statistical convergence in
probabilistic generalized metric spaces (PGMS). Additionally, we define and explore the concept of 
statistical Cauchyness and investigate their interrelationships.

Downloads

Download data is not yet available.

Author Biographies

Ömer Kişi, Bartın University

Department of Mathematics,  Bartın, Turkey

Mehmet Gürdal, Suleyman Demirel University

Department of Mathematics, Isparta, Turkey

Elif Hevesker, Bartın University

Department of Mathematics,  Bartın, Turkey

References

R. Abazari, “Statistical convergence in probabilistic generalized metric spaces wrt strong topology,” J. Inequal. Appl., 2021(1) (2021), 1–11.

H. Çakallı, “New kinds of continuities,” Comput. Math. Appl., 61(2011), 960–965.

S. Das, A. Ghosh, “J-statistical convergence in probabilistic generalized metric spaces“, preprint, 2024.

H. Fast, “Sur la convergence statistique,” Colloq. Math., 2 (1951), 241–244.

M. Gürdal, “Some types of convergence,” Doctoral Dissertation, Suleyman Demirel University, 2004.

M. Gürdal, Ö. Kişi, S. Kolanci, “On generalized statistical convergence in g-metric spaces,” Ilirias J. Math., 10(1) (2023), 1–13.

M. Gürdal, Ö. Kişi, S. Kolanci, “New convergence definitions for double sequences in g-metric spaces,” J. Classical Anal., 21(2) (2023), 173–185.

M. Gürdal, A. Şahiner, “Extremal I-limit points of double sequences,” Appl. Math. E-Notes, 8 (2008), 131-137

S. Kolanci, M. Gürdal, Ö. Kişi, “g-metric spaces and asymptotically lacunary statistical equivalent sequences,” Honam Math. J., 45(3) (2023), 503–512.

K. Menger, Statistical metrics, Proc. Nat. Acad. Sci., 28(1942), 535–537.

M. Mursaleen, “λ-statistical convergence”, Math. Slovaca, 50(1)(2000), 111-115.

Z. Mustafa, H. Obiedat, F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory Appl., 2008(2008), Article ID 189870.

Z. Mustafa, W. Shatanawi, M. Bataineh, “Existence of fixed point results in G-metric spaces,” Fixed Point Theory Appl., 2009(2009), Article ID 283028.

B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific J. Math., 10(1960), 314–334.

B. Schweizer, A. Sklar, E. Thorp, “The metrization of statistical metric spaces,” Pacific J. Math., 10(1960), 673–675.

B. Schweizer and A. Sklar, “Probabilistic Metric Spaces,” iorth Holland, New York, Amsterdam, Oxford, 1983.

R. M. Tardiff, “Topologies for probabilistic metric spaces,” Pacific J. Math., 65(1976), 233–251.

C. Zhou, S. Wang, L. Ciric, S. Alsulami, “Generalized probabilistic metric spaces and fixed point theorems,” Fixed Point Theory Appl., 2014(2014), 1–15.

C. Zhu, W. Xu, Z. Wu, “Some fixed point theorems in generalized probabilistic metric spaces,” Abstr. Appl. Anal., 2014 (2014), 1–8.

Downloads

Published

2024-08-29

How to Cite

Kişi, Ömer, Gürdal, M., & Hevesker, E. (2024). Some Results For Probabilistic Generalized Metric Spaces. International Journal of Advanced Natural Sciences and Engineering Researches, 8(7), 218–227. Retrieved from https://as-proceeding.com/index.php/ijanser/article/view/1989

Issue

Section

Articles