‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...

the main purpose of this paper is to find t-best approximations in fuzzy normed spaces. we introduce the notions of t-proximinal sets and f-approximations and prove some interesting theorems. in particular, we investigate the set of all t-best approximations to an element from a set.

We consider CLS structures as extensions of loop structure as systems 〈 a carrier, a zero, an addition, an external multiplication 〉, where the carrier is a set, the zero is an element of the carrier, the addition is a binary operation on the carrier, and the external multiplication is a function from [: C, the carrier :] into the carrier. Let us observe that there exists a CLS structure which ...

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with inner product 〈·, ·〉 : X ×X → K satisfying • 〈x + y, z〉 = 〈x, z〉+〈y, z〉, • 〈αx, y〉 =α〈x, y〉, • 〈x, y〉 = 〈y, x〉, • 〈x, x〉 ≥ 0 with 〈x, x〉 = 0 ⇐⇒ x = 0. [2] An inner product induces a norm on X via ‖x‖ =p...

The main aim of this paper is to prove a bilateral inequality for P [‖ n ∑ 1 akrk‖ > t ] , where t > 0, (ak) are elements of a normed space, while (rk) are Rademacher functions. Then this inequality is applied for estimation of E‖ n ∑ 1 akrk‖. As another corollary we give a maximal inequality for exchangeable random variables that recently has been published in [4]. 2000 Mathematics Subject Cla...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper we introduce the notion of weak and strong intuitionistic fuzzy (Schauder) basis on an intuitionistic fuzzy n-normed linear space [5] and prove that an intuitionistic fuzzy n-normed linear space having a weak intuitionistic fuzzy basis is separable. Also we discuss approximation property on the same space. Mathematics Subject Classification: 03B20, 03B52, 46A99, 46H25

In this paper, we redefine the notion of fuzzy 2-normed linear space using t-norm and fuzzy anti-2-normed linear space using t-conorm and introduced the definition of intuitionistic fuzzy 2-norm on a linear space. Mathematics Subject Classification: 46S40, 03E72