Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

Researchers who have been responsible for developing test batteries have argued that competent practice requires the use of a "fixed battery" that is co-normed. We tested this assumption with three normative systems: co-normed, meta-regressed norms and a system of these two methods. We analyzed two samples: 330 referred patients and 99 undergraduate volunteers. The T scores generated for referr...

1. Recently I. Gelfand1 has defined a class of characters of Abelian groups embedded in a normed commutative vector ring. The present note contains an elaboration of this theory with a strengthening of the main theorem and extensions to semi-groups. Let 9R be a normed commutative vector ring with unit element e, £ the set of maximal ideals 9 in 9?, 9/9) the corresponding residue class rings eac...

Every continuous linear functional defined on a vector subspace of a real normed space can be extended to the whole space so as to remain linear and continuous, and with the same norm(2). The extension of continuous linear transformations between two real normed spaces has been studied by several authors and for a long time it has been recognized that this problem has a close connection with th...

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...

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...

Let BY denote the unit ball of a normed linear space Y . A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y , there exists a linear projection P : Y → X such that P (BY ) ⊂ A. The main result of the paper is a description of all possible shapes of mi...