  Some fixed point results of classical theory, such as Banach's Fixed Point
Theorem, have been previously extended by other authors to asymmetric spaces in
recent years. The aim of this paper is to extend to asymmetric spaces some
others fixed point results for contractions, shrinkage maps and non-expansive
maps. In fact, a version of Edelstein type theorem (Theorem 21), Schauder type
theorem (Theorem 22), and Kirk type theorem (Theorem 26) are stated and proved
in this new context. In order to do that, classical definitions and results
were adapted to this new context. Also, the normal structure in the asymmetric
case was considered.
