In this paper, we define some classes of double sequences over n-normed spaces by means of an Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.

This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

In this paper, we introduce the concept of λ-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and λ-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, λ)-summability in n-normed spaces.

In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed 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...