On Generalized Normed Spaces

In this paper, we introduce a generalized normed space, which we refer to as a G-normed space. We define the concepts of a G-continuous and a G-bounded linear operator on this space and explore some related properties. Given the central role of the Banach-Steinhaus Theorem in the theory of normed spaces, particularly in the study of bounded linear operators, we conclude by formulating and proving a version of the Banach-Steinhaus Theorem for G-normed spaces.

Keywords:

G-norm , G-continuous , G-bounded , Banach-Steinhaus Theorem