TY  - JOUR
T1  - On the n-Normed Space of Continuous Functions
AU - Amer Kamel, Rehab AU - Ali Kareem, Mayada 
JO  - Journal of Engineering and Applied Sciences
VL  - 14
IS  - 22
SP  - 8312
EP  - 8314
PY  - 2019
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2019.8312.8314
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2019.8312.8314
KW  - particular
KW  -p-summable
KW  -n-normed space
KW  -dual space
KW  -convergence space
KW  -usual norm
AB  - 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 l<sup>p</sup>, the space of p-summable
sequences. The purpose of this study is to study the relation between the two n-norms on L<sub>&infin;</sub>, 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&#146;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<sub>&infin;</sub>.
ER  -