Consider a sum-product normed space, i.e. a space of the form Y = `1 ⊗ X , where X is another normed space. Each element in Y consists of a length-n vector of elements in X , and the norm of an element in Y is the sum of the norms of its coordinates. In this paper we show a constant-distortion embedding from the normed space `1 ⊗X into a lower-dimensional normed space ` ′ 1 ⊗ X , where n′ n is ...

A normed vector space is a real or complex vector space in which a norm has been defined. Formally, one says that a normed vector space is a pair (V, ∥ · ∥) where V is a vector space over K and ∥ · ∥ is a norm in V , but then one usually uses the usual abuse of language and refers to V as being the normed space. Sometimes (frequently?) one has to consider more than one norm at the same time; th...

 The concept of statistical convergence in $2$-normed spaces for double sequence was introduced in [S. Sarabadan and S. Talebi, {it Statistical convergence of double sequences  in $2$-normed spaces }, Int. J. Contemp. Math. Sci. 6 (2011) 373--380]. In the first, we introduce concept strongly statistical convergence in $2$-normed spaces and generalize some results. Moreover,  we define the conce...

In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

the concept of statistical convergence in 2-normed spaces fordouble sequence was introduced in [17]. in the first, we introduceconcept strongly statistical convergence in $2$- normed spaces andgeneralize some results. moreover,  we define the concept of statisticaluniform convergence in $2$- normed spaces and prove a basictheorem of uniform convergence in double sequences to the case ofstatisti...

The purpose of this paper is to introduce and discuss the concept of orthogonality in the fuzzy metric spaces. At last we introduce and discuss the concept of orthogonality in the fuzzy normed spaces, and obtain some results on orthogonality in fuzzy normed spaces similar to orthogonality in normed spaces.

In this paper, we define and study Cheng-Mordeson L-fuzzy normed spaces. Further, we consider the finite dimensional Cheng-Mordeson L-fuzzy normed spaces and prove some theorems about completeness, compactness and weak convergence in these spaces. As application, we get a stability result in the setting of Cheng-Mordeson L-fuzzy normed spaces.

The primary purpose of this paper is to introduce the notion of fuzzy n-normed linear space as a generalization of n-normed space. Ascending family of α-n-norms corresponding to fuzzy n-norm is introduced. Best approximation sets in α-n-norms are defined. We also provide some results on best approximation sets in α-n-normed space.

We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.

Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes. By this additional information, cubical sets can provide a sort of 'noncommutative topology', agreeing with some results of noncommutative geometry but lacking the metric aspects of C*-algebras. Here, we make such similarity stri...