On Generalized Probabilistic Normed Spaces

Some Results in Generalized Serstnev Spaces

On Generalized Probabilistic 2-normed Spaces

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 ...

Menger probabilistic normed space is a category topological vector space

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...

Generalized Statistical Convergence in Probabilistic Normed Spaces

In this paper we define the concepts of λ-statistical convergence and λ-statistically Cauchy in probabilistic normed space and prove some interesting results. Furthermore, we display an example such that our method of convergence is stronger than the usual convergence in probabilistic normed spaces.

On Probabilistic 2-normed Spaces

In [16] K. Menger proposed the probabilistic concept of distance by replacing the number d(p, q), as the distance between points p, q, by a distribution function Fp,q. This idea led to development of probabilistic analysis [3], [11] [18]. In this paper, generalized probabilistic 2-normed spaces are studied and topological properties of these spaces are given. As an example, a space of random va...