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 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.

From now on S, T ,W , Y denote real normed spaces, f , f1, f2 denote partial functions from S to T , Z denotes a subset of S, and i, n denote natural numbers. Now we state the propositions: (1) Let us consider a set X and functions I, f . Then (f X) · I = (f · I) I−1(X). (2) Let us consider real normed spaces S, T , a linear operator L from S into T , and points x, y of S. Then L(x)− L(y) = L(x...

Let X and Y be real normed linear spaces and let φ : X → R be a non-negative function satisfying φ(x+ y) ≤ φ(x) + ‖y‖ for all x, y ∈ X. We show that there exist optimal constants cm,k such that if P : X → Y is any polynomial satisfying ‖P (x)‖ ≤ φ(x)m for all x ∈ X, then ‖D̂kP (x)‖ ≤ cm,kφ(x) whenever x ∈ X and 0 ≤ k ≤ m. We obtain estimates for these constants and present applications to polyno...

The famous R. James’ Theorem (see [3–7] and [8]) asserts that a Banach space E is reflexive if and only if the closed unit ball UE has the James’ property, i.e. every continuous linear functional f of E attains its supremum in UE. James’ Theorem does not hold, however, for general normed spaces [6]. We prove in this talk that a normed space X is reflexive if and only if UX has the separation pr...

In this paper, we introduce difference double sequence spaces ${I_{2} }^{(\mu,\upsilon)}(M,\Delta)$ and ${I_{2}^{0}}^{(\mu,\upsilon)}(M,\Delta)$ in the intuitionistic fuzzy normed linear spaces. We also investigate some topological properties of these