Hanh-Banach theorem, the sandwich theorem for sublinear and superlinear functionals

A linear functional extension that preserves a specified attribute is the ″Hahn-Banach″ Theorem. This means that when we have a linear functional specified on the a subset of a real subspace that is dominated by a sublinear functional over the entire space, we can extend this functional over the entire space that is still controlled by a sublinear functional. In this thesis, we look at the extension of a linear functional given on a subspace of a real linear space that is controlled by a sublinear functional and dominated by a superlinear functional. In addition, we cover various methods for proving the Sandwich Theorem for both sublinear and superlinear functionals.