On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.

The concept of 2-normed spaces was initially developed by Gähler[5] in the mid of 1960’s, while that of n-normed spaces one can see in Misiak[15]. Since then, many others have studied this concept and obtained various results, see Gunawan ([7,8]) and Gunawan and Mashadi [9] and references therein. Let n ∈ N and X be a linear space over the field K, where K is field of real or complex numbers of...

In this paper we established some of the results of the best simultaneous approximation in the context of linear 2-normed space. 2000 Mathematics Subject Classification: 41A50, 41A52, 41A99, 41A28.

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...

Let X be a linear space. A p-norm on X is a real-valued function on X with 0 < p ≤ 1, satisfying the following conditions: (i) ‖x‖p ≥ 0 and ‖x‖p = 0⇔ x = 0, (ii) ‖αx‖p = |α|p‖x‖p, (iii) ‖x+ y‖p ≤ ‖x‖p +‖y‖p for all x, y ∈ X and all scalars α. The pair (X ,‖,‖p) is called a p-normed space. It is a metric linear space with a translation invariant metric dp defined by dp(x, y)= ‖x− y‖p for all x, ...

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...