• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.215-231
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• 2022

In this paper, for double set sequences, as a new approach to the notion of Wijsman asymptotical lacunary statistical equivalence of order 𝜂, we introduce new concepts which are called Wijsman asymptotical ${\mathcal{I}}_2$-lacunary statistical equivalence of order 𝜂 and Wijsman asymptotical strong ${\mathcal{I}}_2$-lacunary equivalence of order 𝜂 where 0 < 𝜂 ≤ 1. Also, some properties of these new concepts are investigated, and the existence of some relations between these and some previously studied asymptotical equivalence concepts for double set sequences is examined.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• 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.