I 2 - λ ¯ -statistically convergence of double sequences in fuzzy normed spaces

Abstract

In this paper, we have investigated ${\mathcal{I}}_2$ - $\overline{\lambda }$ -statistically convergence for double sequences in fuzzy normed linear spaces, where λ = (λ _r ) and μ = (μ _s ) be two non-decreasing sequences of positive real numbers, each tending to ∞ and such that λ _r+1 ≤ λ _r  + 1, λ ₁ = 1; μ _s+1 ≤ μ _s  + 1, μ ₁ = 1. Some inclusion relations between ${\mathcal{I}}_2$ -statistically convergent and ${\mathcal{I}}_2$ - $\overline{\lambda }$ -statistically convergent double sequences in fuzzy normed linear spaces are established. Finally, we have introduced ${\mathcal{I}}_2$ - ${\left[V,\overline{\lambda }\right]}_{\mathit{FN}}$ -summability and ${\mathcal{I}}_2$ -[C, 1]  _FN -summability of double sequences, and then, we have studied the relation between these concepts and $\overline{\lambda }$ -statistical convergence.