ON <i>n</i>-BOUNDED AND <i>n</i>-CONTINUOUS OPERATOR IN <i>n</i>-NORMED SPACE

Abstract

In this paper, the concepts of bounded and continuous n-linear operatorsin n-normed space are discussed. The notions of n-bounded and n-continuous linear operators are then introduced as an extension. This is a generalization of the concepts introduced in [9] and [3]. In addition, the properties of the corresponding spaces of operators are studied to obtain results analogous to the case of normed space. Finally, a sufficient condition for each corresponding space of operators tobe a Banach space is given.

DOI : http://dx.doi.org/10.22342/jims.18.1.109.45-56