and Applied Analysis 3 with f 0 0 in a non-Archimedean space. It is easy to see that the function f x ax bx2 is a solution of the functional equation 1.8 , which explains why it is called additive-quadratic functional equation. For more detailed definitions of mixed type functional equations, we can refer to 26–47 . Definition 1.1 see 48 . Let X be a real vector space. A function N : X × R → 0,...

In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

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 result of the paper is a description of all possible shapes of mi...

Abstract Quite recently, the concept of intuitionistic fuzzy 2-normed spaces was introduced by Mursaleen and Lohani [6]. Also, Mursaleen and Mohiuddine [7] have studied the notion of statistical convergence of double sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy 2...

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.

Let (X,N) be a fuzzy normed space. For each 0 < < 1 and a non-empty subset A of X, we define a natural notion for -farthest points from A and a set-valued map x 7→ Q (A, x), called the fuzzy -farthest point map. Then we will investigate basic properties of the fuzzy -farthest point mapping. In particular, we show that the fuzzy -farthest point map is closable.

The aim of this paper is to give the set of all t-best approximations on fuzzy 2-normed linear spaces and prove some theorems in the sense of Vaezpour and Karimi [13]. AMS Subject Classification: 46A30, 46S40, 46A70, 54A40

We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multimeasures taking values in the family of all closed nonvoid subsets of a real normed space. Key–words: Darboux property, fuzzy multimeasure, atom, non-atomic, regular, diffused.

in this paper, we investigate the generalizedhyers--ulam stability of the functional equation