Journal of Engineering and Applied Sciences
ISSN: Online 1818-7803ISSN: Print 1816-949x
Abstract
In Sixties the concept of 2-normed spaces was initially developed by Gahler while that of n-normed space one can see in Misiak. Since, then many others have studied this concepts and obtained various results. Mutaqin and Gunawan studied the relation between two known n-norms on lp, the space of p-summable sequences. The purpose of this study is to study the relation between the two n-norms on L∞, the space of all 4 continuous functions. The first n-norm is taken from Gunawan definition while the second n-norm is derived from Gahler’s formula. In particular, we examine the convergence in terms of these n-norms and prove that the convergence in terms of each of these n-norms is equivalent to that in the usual norm on L∞.
How to cite this article:
Mayada Ali Kareem and Rehab Amer Kamel. On the n-Normed Space of Continuous Functions.
DOI: https://doi.org/10.36478/jeasci.2019.8312.8314
URL: https://www.makhillpublications.co/view-article/1816-949x/jeasci.2019.8312.8314