Mathematica Eterna
Open Access

Abstract

On the n-Normed Space of p-Integrable Functions

Shelvi Ekariani, Hendra Gunawan and Janny Lindiarni

The space L p (X), where X is a measure space with at least n disjoint subsets of positive measure, can be equipped with an n-norm, which makes L p (X) an n-normed space. The purpose of this paper is to study some properties of this n-normed space. In particular, we examine the completeness of the n-normed space and prove a contractive mapping theorem on this space.