In this article we introduce the notions of I-limit superior and I-limit inferior for sequences in intuitionistic fuzzy normed linear spaces and prove intuitionistic fuzzy analogue of some results of I-limit superior and I-limit inferior for real sequences. The concept of I-limit points and I-cluster points in intuitionistic fuzzy normed linear spaces are introduced and some of their properties...

In this paper level-cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied. Using the extensions of nonlinear compact operators, topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces. As an application of degree theory, a fixed point theorem for condensing operators is presented. © 2009...

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

The goal here is to extend this result to general normed vector spaces over the reals. Informally, a “vector space over the reals,” is a set X together with the operations vector addition and scalar multiplication, which are assumed to have the usual properties (e.g., vector addition is commutative). “Over the reals” means that scalars are in R rather than in some other field, such as the compl...

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.

We develop the theory of Fraïssé limits for classes finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence seminorms. define notion Fréchet space and we use correspondence in this setting obtain many examples such spaces. This allows us give Fraïssé-theoretic construction (Gω,(‖⋅‖n)n<ω), separable almost universal disposition class all ...

We provide a new proof of James’ sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson ([5]) : “If a normed space E does not contain any asymptotically isometric copy of l(N), then every bounded sequence of E′ has a normalized block sequence pointwise converging to 0”.

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...