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

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