Ideal convergent function sequences in random 2-normed spaces

Abstract

In the present paper we are concerned with I-convergence of sequences of functions in random 2-normed spaces. Particularly, following the line of recent work of Karakaya et al. [23], we introduce the concepts of ideal uniform convergence and ideal pointwise convergence in the topology induced by random 2-normed spaces, and give some basic properties of these concepts.

$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces

“…Now, we recall the concept of density, statistical convergence, 2-normed space and some fundamental definitions and notations (See [1,2,4,6,16,17,18,20,21,22,23,24,25,26,29,30,31,37,38,40]). Let X be a real vector space of dimension d, where 2 ≤ d < ∞.…”

On the Lacunary Statistical Convergence of Triple Sequences in Fuzzy Metric Spaces

“…Fridy and Orhan defined the concept of lacunary statistical convergence [7]. Various applications of this concept can be found in [3,6,10,16,20,21,22,23,24,27,28,29,30,32,33].…”

I-Localized Sequences in Metric Spaces

“…Also, in this case I and I * -Cauchy sequences are the same (see [8]). More property and fact about ideal convergence and statistical convergence are contained, for instance, in Gürdal et al [2], Nuray et al [10], Savaş and Gürdal [11,12], Şahiner et al [13] and Yegül and Dündar [14].…”