Statistical Convergence with Rough I3-Lacunary and Wijsman Rough I3-Statistical Convergence in 2-Normed Spaces

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DOI: https://doi.org/10.28924/2291-8639-22-2024-115
Published: Jul 19, 2024
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M.H.M. Rashid, Sameer A. Al-Subh, Statistical Convergence with Rough I3-Lacunary and Wijsman Rough I3-Statistical Convergence in 2-Normed Spaces, Int. J. Anal. Appl., 22 (2024), 115.

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M.H.M. Rashid, Sameer A. Al-Subh

Abstract

In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2-normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points and its rough I3-lacunary statistical limit points in the same 2-normed space. Expanding upon the concept of triple sequence spaces, we have introduced the notion of Wijsman I3-Cesáro summability for triple sequences. In doing so, we have investigated the connections between Wijsman strongly I3-Cesáro summability and Wijsman statistical I3-Cesáro summability. Furthermore, we have introduced the concepts of Wijsman rough strongly p-lacunary summability of order α and Wijsman rough lacunary statistical convergence of order α for triple sequences. These new concepts have been subjected to a thorough examination to understand their characteristics, and we have explored potential connections between them. Additionally, we have investigated how these newly introduced concepts relate to existing notions in the literature.

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