In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of R, and we discuss their extension to E. We introduce the notion of E-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of con...

In the present paper, we prove that the classical sets ∞(F ), c(F ), c0(F ) and p(F ) of sequences of fuzzy numbers are normed quasilinear spaces and the β−, α−duals of the set 1(F ) is the set ∞(F ). Besides this, we show that ∞(F ) and c(F ) are normed quasialgebras and an operator defined by an infinite matrix belonging to the class ( ∞(F ) : ∞(F )) is bounded and quasilinear. Finally, as an...

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. Keywords—Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best ...

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

Fuzzy anti-bounded linear functional and fuzzy antidual spaces are defined. Hahn-Banach theorem and some of its consequences on fuzzy anti-normed linear space are studied. Two fundamental theorems; namely, open mapping theorem and closed graph theorem are established. Keywords-Fuzzy anti-norm, α-norm, Fuzzy anti-complete, Fuzzy anti-bounded linear functional, Fuzzy anti-dual space.

1 Definitions and Examples 1.1 Metric and Normed Spaces Definition 1.1. A metric space is a pair (X, d), where X is a set and d is a function from X ×X to R such that the following conditions hold for every x, y, z ∈ X. 1. Non-negativity: d(x, y) ≥ 0. 2. Symmetry: d(x, y) = d(y, x). 3. Triangle inequality: d(x, y) + d(y, z) ≥ d(x, y) . 4. d(x, y) = 0 if and only if x = y. Elements of X are call...

In [6], the second author proved general metatheorems for the extraction of effective uniform bounds from ineffective existence proofs in functional analysis, more precisely from proofs in classical analysis A(:= weakly extensional Peano arithmetic WE-PA in all finite types + quantitifer-free choice + the axiom schema of dependent choice DC) extended with (variants of) abstract bounded metric s...

in this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

In this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

in this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. the first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. they improve thecorresponding  conclusions in the literature.