Definition 1.3 (Banach Spaces). It is easy to show that any convergent sequence in a normed linear space is a Cauchy sequence. However, it may or may not be true in an arbitrary normed linear space that all Cauchy sequences are convergent. A normed linear space X which does have the property that all Cauchy sequences are convergent is said to be complete. A complete normed linear space is calle...

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...

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...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

In this paper, we obtain a characterization of linear spaces which may be normed so as to become complete, linear, normed metric spaces. In this connection, K. Kunugui and M. Fréchet have shown that every metric space S is isometric with a subset of a complete, linear, normed metric space. I t follows from our result that if the cardinal number of 5 is the limit of a denumerable sequence of car...

Many personality assessment inventories provide gender-specific norms to allow comparison of an individual's standing relative to others of the same gender. In some cases, this means that an identical raw score produces standardized scores that differ notably depending on whether the respondent is male or female. Thus, an important question is whether unisex-normed scores or gender-normed score...

and Applied Analysis 3 The condition of right K-completeness for X, p leaves outside the scope of this theorem an important class of asymmetric normed spaces, the asymmetric normed spaces associated to normed lattices because these spaces are right K-complete only for the trivial case 13 . In this paper, we give a uniform boundedness type theorem in the setting of asymmetric normed spaces which...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...