Note on KKM maps and applications

In this thesis, KKM mappings and some applications in topological vector and abstract convex spaces have been studied. At first, background information, some basic definitions and theorems were given. Then semi-continuous on single valued and multivalued mappings were given fundamentally. In topological vector spaces, KKM mapping and some applications were given and fixed point has been studied. In general, abstract convex spaces were introduced and the relation between KKM spaces and abstract convex spaces has been emphasized. Also equivalents of some applications of KKM mappings in abstract convex spaces were shown. Lastly fixed point and coincidence point on some applications of KKM mappings in normed spaces have been studied.