Lacunary invariant statistical equivalence for double set sequences

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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