Locally Quasiconvex Spaces and Fixed Point Theorems

Abstract

We introduced the notions of \emph{locally quasiconvex spaces} and \emph{quasi-seminorms,} and investigate the natural relationships between these two notions. As applications, we obtain generalizations of some well known fixed point theorems and fixed set theorems that require neither metrizability, nor compactness nor the standard notion of convexity.