In this paper, we investigate the Hyers-Ulam stability of additive functional equations of two forms: of “Jensen” and “Jensen type” in the framework of multi-normed spaces. We therefore provide a link between multi-normed spaces and functional equations. More precisely, we establish the Hyers-Ulam stability of functional equations of these types for mappings from Abelian groups into multi-norme...

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

n this paper we study the hyers-ulam-rassias stability of cauchyequation in felbin's type fuzzy normed linear spaces. as a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. this shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

in this paper, we shall define and study the concept of  -statistical convergence and  -statistical cauchy inrandom 2-normed space. we also introduce the concept of  -statistical completeness which would provide amore general frame work to study the completeness in random 2-normed space. furthermore, we also prove some new results.

A normed vector space is a real or complex vector space in which a norm has been defined. Formally, one says that a normed vector space is a pair (V, ∥ · ∥) where V is a vector space over K and ∥ · ∥ is a norm in V , but then one usually uses the usual abuse of language and refers to V as being the normed space. Sometimes (frequently?) one has to consider more than one norm at the same time; th...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

The aim of this paper is to study the generalization of the intuitionistic fuzzy normed spaces such as intuitionistic fuzzy 2-normed space. In this structure, we have discussed the intuitionistic fuzzy 2continuity and intuitionistic fuzzy 2-boundedness. Also, we have introduced the intuitionistic fuzzy ψ-2-normed space which is a generalization of intuitionistic fuzzy 2-normed space. We have di...

Consider a sum-product normed space, i.e. a space of the form Y = `1 ⊗ X , where X is another normed space. Each element in Y consists of a length-n vector of elements in X , and the norm of an element in Y is the sum of the norms of its coordinates. In this paper we show a constant-distortion embedding from the normed space `1 ⊗X into a lower-dimensional normed space ` ′ 1 ⊗ X , where n′ n is ...

Abstract. Generalizing Pisier’s idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten class. In general, a pair of symmetric normed ideals that are not necessarily the Schatten class may give rise to an operator space...