In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

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.

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 ...

One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al. [12]. In this paper, we define and study the concept of I-convergence, I∗-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I ∗ 2 -convergence, i.e., we show that I ∗ 2 -convergence...

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.