DOI: 10.2478/s12175-011-0059-5 Math. Slovaca 61 (2011), No. 6, 933–940 ON I -CONVERGENCE IN RANDOM 2-NORMED SPACES M. Mursaleen* — Abdullah Alotaibi** (Communicated by Wladyslaw Wilczynski ) ABSTRACT. Recently the concepts of statistical convergence and ideal conver- gence have been studied in 2-normed and 2-Banach spaces by various authors. In this paper we define and study the notion of ideal convergence in random 2-normed space and construct some interesting examples. c 2011 Mathematical Institute Slovak Academy of Sciences 1. Introduction and preliminaries The idea of statistical convergence was introduced by Fast [4] and since then several generalizations and applications of this concept have been investigated by various authors. One of its generalizations is the ideal convergence or I -con- vergence which was introduced by Kostyrko et al [11] and studied by Balcerzak et al [2], Das et al [3], and Komisarski [12]. Recently, Karakus [10] studied the concept of statistical convergence in probabilistic normed spaces. The theory of probabilistic normed spaces was initiated and developed in [1], [14], [18], [19] and further it was extended to random/probabilistic 2-normed spaces [8] by using the concept of 2-norm [7]. Recently, statistical convergence and I -convergence have been studied in 2-Banach and 2-normed spaces in [9] and [17]. In this paper we define and study I -convergence in random 2-normed space which is quite a new and interesting idea to work with. For the study of statistical convergence and I -convergence of double sequences we refere to [3], [13], [15] and [16]. 2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 40A05; Secondary 46A70, 40A99, 46A99. Keywords: t-norm, random 2-normed space, statitical convergence, I -convergence. AUTHOR COPY