Authors : Rehab Amer Kamel and Mayada Ali Kareem
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∞.
Rehab Amer Kamel and Mayada Ali Kareem, 2019. On the n-Normed Space of Continuous Functions. Journal of Engineering and Applied Sciences, 14: 8312-8314.