Article ID: MTJPAM-D-25-00075

Title: Tri-sequential statistical convergence controlled by triplet of parameters in topological spaces


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-25-00075; Volume 7 / Issue 4 / Year 2025, Pages 55-63

Document Type: Research Paper

Author(s): Prasenjit Bal a , Tanmayee Datta b

aDepartment of Mathematics, ICFAI University Tripura, Kamalghat(799210), West Tripura, India

bDepartment of Mathematics, ICFAI University Tripura, Kamalghat(799210), West Tripura, India

Received: 17 March 2025, Accepted: 8 February 2026, Published: 29 August 2026

Corresponding Author: Prasenjit Bal (Email address: balprasenjit177@gmail.com)

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Abstract

In the framework of topological spaces, the concept of statistical convergence of triple order for triple sequences is investigated. The classical notion of statistical convergence is extended by incorporating three parameters, where parameters lie between zero and one, allowing for a more precise analysis of the convergence behavior of triple sequences. Additionally, the properties of this mode of convergence are examined within the setting of product spaces, with a particular focus on the influence of the topological structure of such spaces on statistical convergence. The main results include the derivation of necessary and adequate conditions for statistical convergence of triple order, the establishment of relationships between this generalized form of convergence and existing notions in the literature, and the analysis of the impact of product spaces on these convergence properties.

Keywords: Asymptotic density, statistical convergence of order α, statistical convergence of order (α, β), statistical convergence of order (α, β, γ), product space

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Cite this article

How to cite this article: P. Bal and T. Datta, Tri-sequential statistical convergence controlled by triplet of parameters in topological spaces, Montes Taurus J. Pure Appl. Math. 7 (4), 55-63, 2025; Article ID: MTJPAM-D-25-00075.