Banach-Steinhaus theorem for linear relations on asymmetric normed spaces

Abstract

We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.

Keywords

• linear relation
• multivalued linear operator
• asymmetric norm