A Generalization of the Hahn-Banach Theorem in Seminormed Quasilinear Spaces

Abstract

The concept of normed quasilinear spaces which is a generalization of normed linear spaces gives us a new opportunity to study with a similar approach to classical functional analysis. In this study, we introduce the notion of seminormed quasilinear space as a generalization of normed quasilinear spaces and give various auxiliary results and examples. We present an analog of Hahn-Banach theorem, in seminormed quasilinear spaces. AMS Subject Classification: 06B99, 32A70, 46A22, 46A99, 46B40, 47H04, 54F05.