\(\mathcal{I}_2\)-Cauchy double sequences in 2-normed spaces

Abstract

The concept I-Cauchy and I * -Cauchy sequences were studied by Gürdal and Ac . ık in [On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11 (2) (2008), [349][350][351][352][353][354]. In this paper, we introduce the notions of I2-Cauchy and I * 2 -Cauchy double sequences, and study their some properties with the property (AP2) in 2-normed spaces.

On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces

“…Now we introduce logarithmic summability in IFNS and prove corresponding Tauberian theorems. For some other studies concerning logarithmic summability and convergence methods in fuzzy setting see [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Regularly ideal convergence and regularly ideal cauchy double sequences in 2-normed spaces

“…They also examined the concepts I 2 -limit points and I 2 -cluster points in 2-normed spaces. Dündar and Sever [5] introduced the notions of I 2 and I * 2 -Cauchy double sequences, and studied their some properties with (AP2) in 2-normed spaces.…”

“…A double sequence x = (x mn ) in X is said to be I * 2 -Cauchy sequence if there exists a set M ∈ F (I 2 ) (i.e., H = N × N\M ∈ I 2 ) such that for each ε > 0 and for all (m, n), (s, t) ∈ M, x mn − x st , z < ε, for each nonzero z in X, where m, n, s, t > k 0 = k 0 (ε) ∈ N. In this case we write lim m,n,s,t→∞ x mn − x st , z = 0. Now, we begin with quoting the following lemmas due to Sarabadan et al [24] and Dündar, Sever [5] which are needed throughout the paper.…”