For simplicity, we follow the rules: X, X1 denote sets, r, s denote real numbers, z denotes a complex number, R1 denotes a real normed space, and C1, C2, C3 denote complex normed spaces. Let X be a set, let C2, C3 be complex normed spaces, and let f be a partial function from C2 to C3. We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X...

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...

A mapping α from a normed space X into itself is called a Banach operator if there is a constant k such that 0≤ k < 1 and ‖α2(x)−α(x)‖ ≤ k‖α(x)−x‖ for all x ∈X. In this note we study some properties of Banach operators. Among other results we show that if α is a linear Banach operator on a normed space X, then N(α−1) = N((α−1)2), N(α−1)∩R(α−1)= (0) and if X is finite dimensional then X =N(α−1)⊕...

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 results of the paper: (1) Each minimal-volume sufficient enlargem...

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...

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.

In this paper, we use the denition of fuzzy normed spaces givenby Bag and Samanta and the behaviors of solutions of the additive functionalequation are described. The Hyers-Ulam stability problem of this equationis discussed and theorems concerning the Hyers-Ulam-Rassias stability of theequation are proved on fuzzy normed linear space.

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...

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.

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...