Topological insights into weighted statistical convergence for triple sequence
Abstract
This research explores the concept of weighted statistical convergence for triple sequences under a topological perspective, an extension of weighted statistical convergence by incorporating three weight functions $g, h$ and $i$ into the framework, refining the notion of convergence to accommodate variations in density and distribution of sequence elements. The study examines the properties and behaviors of these sequences, emphasizing their applications in topology. We provide characterizations, theorems, and examples to illustrate the nuanced convergence criteria under different topological settings, highlighting the impact of weights on convergence rates and patterns. This generalized approach offers deeper insights and more flexible tools for analyzing convergence in complex structures. The work also discusses the product spaces, which play a critical role in understanding the interaction and convergence properties of multiple sequences simultaneously. By leveraging the structure of product spaces, the study provides a comprehensive view of how triple sequences converge under three weight functions and topological features.
Downloads
References
Adem, A. A., Altinok, M., Weighted statistical convergence of real valued sequences, Facta Universitatis Ser. Math. Info., 35 no. 3, 887-898, (2020).
Bal, P., Rakshit, D., A variation of the class of statistical γ covers, Topological Algebra and its applications, 11, 20230101, (2023).
Bal, P., Datta, T., Das, P., Statistical convergence of order α and it’s application to selection principles, Comment. Math. Univ. Carol, (2024) (Accepted).
Balcerzak, M., Das, P., Filipczak, M., Swaczyna, J., Generalized kinds of density and the associate ideals, Acta Math. Hungar., 147, no. 1, 97-115, (2015).
Bhunia, S., Das, P., Pal, S. K., Restricting statistical convergence, Acta Math. Hungar., 134 (1-2), 153-161, (2012).
Buck, R. C., Generalized Asymptotic density, Amer. J. Math., 75, 335-346, (1953).
C¸ olak, R., Statistical convergence of order α, Modern Methods in Analysis and Its Applications (M. Mursaleen, ed.), Anamaya Publication, pp. 121-129, (2010).
Das, P., Bal, P., Statistical Convergence Restricted by Weight Functions and its Application in the Variation of γ-covers, Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste, 56, (2025).
Engelking, R., General Topology, Heldermann Verlag, Berlin, (1989).
Fast, H., Sur la convergence statistique, Colloq. Math., 2, 241-244, (1951).
Kwela, A., Poplawski, M., Swaczyna, J., Tryba, J., Properties of simple density ideals, J.Math. Anal. Appl., 477 no. 1, 551-575, (2019).
Maio, G. D., Kocinac, L. D. R., Statistical Convergence in Topology, Topology and its applications, 156, 28-45, (2008).
Mursaleen, M., Edely, O. H. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288, 223-231, (2003).
Sahiner, A., Gurdal, M., Duden, F. K., Triple sequences and their statistical convergence, Selcuk J. Appl. Math., 8 No. 2, pp. 49-55, (2007).
Schoenberg, I. J., Integrability of certain functions and related summability methods,, Amer. Math. Monthly, 66, 361–375, (1959).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
