The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

The claim that follows, which I have called the nite-dimensional normed linear space theorem, essentially says that all such spaces are topologically R with the Euclidean norm. This means that in many cases the intuition we obtain in R,R, and R by imagining intervals, circles, and spheres, respectively, will carry over into not only higher dimension R but also any vector space that has nite dim...

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...

Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {T : A → 2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T (x) : x ∈ A} is nonempty. Using this nonempty intersection theorem, we attempt...

We investigate a new notion of embedding of subsets of {−1, 1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, ..., n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {−1, 1}n, the vast majority of such sets do not embed i...

In this paper, we give some properties of the sets Be(a, r) and Be[a, r]. This enables us to obtain a result analogue of “Open mapping theorem”for 2-normed space 2000 Mathematics Subject Classification: 41A65, 41A15.

Fuzzy set theory is a useful tool to describe situations in which the data are imprecise or vague. Fuzzy sets handle such situation by attributing a degree to which a certain object belongs to a set. The idea of fuzzy norm was initiated by Katsaras in [1984]. Felbin [1992] defined a fuzzy norm on a linear space whose associated fuzzy metric is of Kaleva and Seikkala type [1984]. Cheng and Morde...

A common xed theorem is proved for two pairs of compatible mappings on a normed vector space.