• A GENERALIZATION OF HAHN-BANACH THEOREM

Abstract

We present a generalization of Hahn-Banach extension theorem. In this paper, we introduce the notion of -convex function, and provide an proof for the new version of the Hahn-Banach theorem which says that if a linear operator defined on a subspace of a real vector space is dominated by a -convex function defined on , then it has a linear extension which is also dominated by the same -convex operator defined on .

Key words: Hahn-Banach theorem, linear subspaces, -convex function.

AMS subject classifications: 90C25, 90C33