• Honam Mathematical Journal
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• v.45 no.3
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• pp.555-571
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• 2023

The main purpose of this paper is to introduce the concept of asymptotical deferred statistical equivalence in the Wijsman sense for double set sequences. Also, we give some properties of this concept and prove some theorems associated with this concept. Furthermore, we examine the connection between the concepts of asymptotical deferred statistical and Cesàro equivalence in the Wijsman sense for double set sequences.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.485-499
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• 2024

In this paper, we propose the concepts of asymptotic equivalence, asymptotic statistical equivalence, lacunary statistical equivalence of order (α, β) in sense of Wijsman. We also make an effort to define these concepts by using modulus function with respect to ideal ${\mathcal{I}}$ and examine some algebraic and topological properties related to these concepts.