n-Boundedness and n-Continuity of Linear Operators

Abstract

The concept of n-bounded and n-continuous operators is discussed as an extension of the concept introduced in [12]. The equivalence of three statements on n-continuity and n-boundedness of a linear operator from a normed space into an n-normed space is also proved. This newly introduced concept is proved to be identical to one type of n-continuity introduced in [12].