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DOUBLE WIJSMAN LACUNARY STATISTICAL CONVERGENCE OF ORDER 𝛼
GULLE, ESRA,ULUSU, UGUR The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.3
In this paper, we introduce the concepts of Wijsman strongly p-lacunary summability of order 𝛼, Wijsman lacunary statistical convergence of order 𝛼 and Hausdorff lacunary statistical convergence of order 𝛼 for double set sequences. Also, we investigate some properties of these new concepts and examine the existence of some relationships between them. Furthermore, we study the relationships between these new concepts and some concepts in the literature.
GULLE, ESRA,ULUSU, UGUR The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.1-2
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.
( Erdinç Dündar ),( Nimet Pancaroğlu Akin ),( Ugur Ulusu ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
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.