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...

s In respect of the de finition of intuitionistic fuzzy n-norm [9] , the definition of generalised intuitionistic fuzzy ψ norm ( in short GIFψN ) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy ψ normed linear space and finite dimensional generalized intuitionistic fuzzy ψ normed linear space have been developed. Lastly, we have introduced the...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1≤p≤∞, respectively, and prove that ℓpλ(B) and ℓ p are linearly isomorphic for 0<p≤∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1≤p<∞. Furthermore, we determine the alpha-, beta- and gamm...

In this article, we studied the best approximation in probabilistic 2-normed spaces. We defined the best approximation on these spaces and generalized some definitions such as set of best approximation, Pb-proximinal set and Pb-approximately compact and orthogonality relative to any set and proved some theorems about them. AMS Mathematics Subject Classification (2010): 54E70, 46S50

Normed Space [1, 2, §2]. A norm ‖·‖ on a linear space (U ,F) is a mapping ‖·‖ : U → [0,∞) that satisfies, for all u,v ∈ U , α ∈ F , 1. ‖u‖ = 0 ⇐⇒ u = 0. 2. ‖αu‖ = |α| ‖u‖. 3. Triangle inequality: ‖u+ v‖ ≤ ‖u‖+ ‖v‖. A norm defines a metric d(u,v) := ‖u− v‖ on U . A normed (linear) space (U , ‖·‖) is a linear space U with a norm ‖·‖ defined on it. • The norm is a continuous mapping of U into R+. ...