Some fixed point theorems for nonconvex spaces

Abstract

We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces.

Keywords

• Fixed points
• nonconvex topological vector spaces
• multifunctions.