In this paper, we shall define and study the concept of  -statistical convergence and  -statistical Cauchy in random 2-normed space. We also introduce the concept of  -statistical completeness which would provide a more general frame work to study the completeness in random 2-normed space. Furthermore, we also prove some new results.

in the present paper, we study some properties of fuzzy norm of linear operators. at first the bounded inverse theorem on fuzzy normed linear spaces is investigated. then, we prove hahn banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. finally the set of all compact operators on these spaces is studied.

in this paper, we prove the generalized hyers--ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy banach spaces.

and Applied Analysis 3 a vector space from various points of view 28–30 . In particular, Bag and Samanta 31 , following Cheng and Mordeson 32 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 33 . They established a decomposition theorem of a fuzzy norm into a family of crisp norms and investigated some properties of fuzzy normed ...

We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

Let X be a non empty complex normed space structure and let s1 be a sequence of X. The functor ( ∑ κ α=0(s1)(α))κ∈N yielding a sequence of X is defined as follows: (Def. 1) ( ∑ κ α=0(s1)(α))κ∈N(0) = s1(0) and for every natural number n holds ( ∑ κ α=0(s1)(α))κ∈N(n + 1) = ( ∑ κ α=0(s1)(α))κ∈N(n) + s1(n + 1). One can prove the following proposition (1) Let X be an add-associative right zeroed rig...

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. In Patterson and Savas (2006) extended the definitions presented in (Patterson, 2003) to l...

In [1] C. Alsina, B. Schweizer and A. Sklar gave a new definition of a probabilistic normed space. This definition, is based on a characterization of normed spaces by a betweenness relation and put the theory of probabilistic normed spaces on a new general basis. Starting from this idea we study from a new and more general point of view the probabilistic 2-normed spaces. Topological properties ...

The purpose of this paper is to introduce and discuss the concept of orthogonality in normed spaces. A concept of orthogonality on normed linear space was introduced. We obtain some subspaces of Banach spaces which are topologically complemented.

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of Dcompactness and D-boundedness in probabilistic normed spaces.