Rehab  Amer Kamel, Mayada  Ali Kareem, 
    On the n-Normed Space of Continuous Functions,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 22,
    2019,
    Pages 8312-8314,
    ISSN 1816-949x,
    jeasci.2019.8312.8314,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.8312.8314)
    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 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>.
    Keywords: particular;p-summable;n-normed space;dual space;convergence space;usual norm