Fixed point theorems for the class S-KKM mappings in abstract convex spaces

We define KKM mappings and S-KKM mappings similarly to in the case of convex spaces for abstract convex spaces. Some approximate fixed point theorems will be established for the multifunction with the S-KKM property on ΦΦ-spaces. We also obtain a new version of Sadovskii’s fixed point theorem in topological spaces.