Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆-statistical convergence and lacunary ∆-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. Subjclass [2000] : Primary 40A05; Secondary 46A70, 40A99, 46A99.

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

We show that, given an n-dimensional normed space X a sequence of N = (8/ε)2n independent random vectors (Xi)i=1, uniformly distributed in the unit ball of X∗, with high probability forms an ε net for this unit ball. Thus the random linear map Γ : Rn → RN defined by Γx = (〈x,Xi〉)i=1 embeds X in `∞ with at most 1+ ε norm distortion. In the case X = `2 we obtain a random 1 + ε embedding into `∞ w...

P.Kostyrko et al [10] introduced the concept of Iconvergence of sequence in metric space and studied some properties of such convergence. Since then many author have been studied these subject and obtained various results [29,30,31,32,?] Note that I-convergence is an interesting generalization of statistical convergence. The concept of 2-normed space was initially introduced by Gähler [7] as an...

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...

We extend the Khinchin–Kahane inequality to an arbitrary abelian metric group G . In the special case where G is normed, we prove a refinement which is sharp and which extends the sharp version for Banach spaces. We also provide an alternate proof for normed metric groups as a consequence of a general “transfer principle”. This transfer principle has immediate applications to stochastic inequal...

In this paper, generalized probabilistic n-normed spaces are studied, topological properties of these spaces are given. As examples, spaces of random variables are considered. Connections with generalized deterministic n-normed spaces are also given. Mathematics Subject Classification: 60H10, 47H10

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...