Some results of fixed point of non-expansive mappings on asymmetric spaces

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.