WEIGHTED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN TOPOLOGY

Document Type : Original Manuscript

Authors

Department of Mathematics, ICFAI University Tripura, Kamalghat, West Tripura, INDIA-799210.

10.22044/jas.2025.15549.1921

Abstract

This research extends the concept of double weighted statistical density of two-dimensional natural number sequences, or double sequences, utilizing two weight functions g and h all within the context of topological spaces. We explore the product space of double weighted statistical convergence, providing a comprehensive framework for analyzing convergence behavior in this more complex setting. Additionally, we introduce and examine the concepts of double weighted limit points and double weighted cluster points. This work broadens the understanding of convergence in topological spaces, ordering new tools and perspectives for dealing with sequences infuenced by multiple weighting schemes.

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References

 1. A. A. Adem and M. Altinok, Weighted statistical convergence of real valued sequences, Facta Univ. Ser. Math. Inform., 35(3) (2020), 887–898.
 
2. P. Bal and L. D. R. Kočinac, On selectively star-ccc spaces, Topology Appl., 281 (2020), Article No. 107184.
 
3. S. Bhunia, P. Das and S. K. Pal, Restricting statistical convergence, Acta Math. Hungar., 134(1-2) (2012), 153–161.
 
4. R. Çolak and Ç. A. Bektaş, λ-statistical convergence of order α, Acta Math. Sci. Ser. B., 31(3) (2010), 953–959.
 
5. J. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47–63.
 
6. P. Das and P. Bal, Statistical convergence restricted by weight functions and its application in the variation of γ-covers, Rend. Istit. Mat. Univ. Trieste, 56 (2024), Article No.11.
 
7. T. Datta, P. Bal and P. Das, Statistical convergence of order α and it’s application to selection principles, Comment. Math. Univ. Carolin., (In press).
 
8. D. Djurčić, Lj. D. R. Kočinac and M. R. Žižović, Double sequences and selections, Abstr. Appl. Anal., 2012 (2012), Article ID: 497594.
 
9. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
 
10. H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
 
11. L. D. R. Kočinac and M. H. M. Rashid, On ideal convergence of double sequences in the topology induced by a fuzzy 2-norm, TWMS J. Pure Appl. Math., 8(1) (2017), 97–111.
 
12. G. D. Maio and L. D. R. Kočinac, Statistical Convergence in Topology, Topology Appl., 156 (2008), 28–45.
 
13. M. Mursaleen and O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231.
 
14. D. Rakshit, P. Bal and T. Datta, Statistical convergence of order (α; β) of double sequence in topology, (submitted).
 
15. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375. 
Journal of Algebraic Systems
Volume 14, Issue 4
September 2026
Pages 683-699

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