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 … Show more
“…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]). …”
Section: Definitions and Notationsmentioning
confidence: 99%
“…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.…”
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.
“…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]). …”
Section: Definitions and Notationsmentioning
confidence: 99%
“…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.…”
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.
“…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].…”
In this article, we propose to determine some stability results for the functional equation of cubic in random 2-normed spaces which seems to be a quite new and interesting idea. Also, we define the notion of continuity, approximately and conditional cubic mapping in random 2-normed spaces and prove some interesting results.
“…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].…”
In the present paper we are concerned with I-statistically pre-Cauchy double sequences in line of of Das et al. [5]. Particularly, we prove that for double sequences, I-statistical convergence implies I-statistical pre-Cauchy condition and examine some main properties of these concepts.
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