Lacunary invariant statistical equivalence for double set sequences

Year 2022, Volume: 71 Issue: 1, 1 - 12, 30.03.2022

Uğur Ulusu , Erdinç Dündar , Nimet Pancaroğlu Akın

https://doi.org/10.31801/cfsuasmas.903988

Abstract

In this paper, we introduce the notions of asymptotical strong ${\sigma }_2$-equivalence, asymptotical ${\sigma }_2$-statistical equivalence, asymptotical lacunary strong ${\sigma }_2$-equivalence and asymptotical lacunary ${\sigma }_2$-statistical equivalence in the Wijsman sense for double set sequences. Also, we investigate some relations between these new asymptotical equivalence notions.

Keywords

Asymptotical equivalence, double lacunary sequence, invariant mean, statistical convergence, convergence in the Wijsman sense

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