F-normed spaces and linear operators

In this article, we generalize some results about norms and linear operators on normed spaces. We first present some results about norms. Then we consider conditions for continuity of an f-norm on a locally convex space. Finally we give some properties of the Minkowski 2-functional of 2-convex, balanced and absorbing subsets of a linear space which are defined with respect to the f-norm.