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Lacunary Statistical Equivalence of Order \(\eta\) for Double Sequences of Sets

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Abstract

In this study, by introducing the concepts of asymptotical lacunary statistical and asymptotical strong p-lacunary equivalence of order \(\eta \) (\(0<\eta \le 1\)) in the Wijsman sense for double set sequences, some properties of these concepts are examined and also the relationship between these concepts is mentioned. Moreover, the relationships between these concepts and the asymptotical equivalence concepts previously given for double set sequences are investigated.

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Authors and Affiliations

  1. Sivas Cumhuriyet University, 58140, Sivas, Turkey

    Uğur Ulusu

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  1. Uğur Ulusu
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Correspondence to Uğur Ulusu.

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Significant Statement

In this paper, we present the concepts of rate of convergence and degree of approximation of any two real or complex sequences, the asymptotical statistical and asymptotical lacunary statistical equivalence in the Wijsman sense for double sequences of sets and tried to explain them with examples.

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Ulusu, U. Lacunary Statistical Equivalence of Order \(\eta\) for Double Sequences of Sets. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 331–337 (2023). https://doi.org/10.1007/s40010-023-00818-y

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  • DOI: https://doi.org/10.1007/s40010-023-00818-y

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