The definitions of S-KKM property and $\Gamma$-invariable property for multi-valued mapping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally $G$-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff $\Phi$-space is proved. Our results improve and generalize the corresponding results in recent literatures.
