The Horofunction Boundary of Finite-dimensional Normed Spaces

Horoballs in simplices and Minkowski spaces

Our interest in horoballs comes on the one hand from the problem of describing the dynamics of certain important classes of self-maps of convex cones, and on the other hand from the work of Rieffel [17] on quantum metric spaces in the context of Connes’ noncommutative geometry. Horofunctions also appeared recently in a general law of large numbers for random walks on groups [11]. As is remarked...

SOME RESULTS ON INTUITIONISTIC FUZZY SPACES

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...

Some Results in Generalized Serstnev Spaces

D-boundedness and D-compactness in finite dimensional probabilistic normed spaces

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.