On ℐ-Cauchy sequences in 2-normed spaces

Abstract

Abstract. The concept of I -convergence is a generalization of statistical convergence and it is depended on the notion of the ideal I of subsets of the set N of positive integers. In this paper for sequences in 2 -normed space the relationship between I -convergence and usual convergence along a filter F (I ) associated with an admissible ideal I with property (AP) is investigated. We introduce the concepts I -Cauchy and I * -Cauchy sequences in 2 -normed spaces and study their certain properties.Mathematics subject classification (2000): 40A05, 46A70, 40A99, 46A99.

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

“…Now, we recall the concept of 2-normed space, ideal, ideal convergence of the sequences, double sequences and some fundamental definitions and notations (See [1,2,7,10,12,14,[21][22][23]). …”

“…Gürdal and Ac . ık [12] investigated I-Cauchy and I * -Cauchy sequences in 2-normed spaces. Sarabadan et al [22,23] investigated I and I * -convergence of double sequences in 2-normed spaces.…”

On the stability of a cubic functional equation in random 2-normed spaces

“…that is associative, commutative nondecreasing and which has ε 0 as unit, that is, for all f, g, h Δ + , we have: The concept of 2-normed space was first introduced in [17] and further studied in [23][24][25].…”

I-statistically pre-Cauchy double sequences

“…Recently, in [4,21], Savaş et al studied the I-statistically convergence of sequences and obtained some results of this concept. For more informations about I-convergence and I-statistically convergence, see [6,5,12,15,19,20,24,27].…”