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...

In this work, we introduce a new 2-norm generated by bounded linear functionals on normed space X with dimension dim(X) ? 2, and investigate its relationship the G?hler?s [Lineare 2-normierte R?ume, Math. Nachr.]. We also derive norm to explore relation usual X.

Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$.  We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all  fuzzyuniquely remotal sets are singletons.

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed s...

In this paper, we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics. We prove the constructive substitutes for the classically well-known theorems on compact linear mappings: T is compact if and only if T* is compact; if S is bounded and if T is compact, then TS is compact; if S and T is compact, then S+ T is compact.

We define the (w∗-) boundedness property and the (w∗-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w∗-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of tw...

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.