The subject matter of this thesis is to investigate the fixed points for generalized KKM mappings on almost convex sets. We obtain the following new fixed point theorem :

Let X be an almost convex subset of a locally convex space E. If T $in$ KKM(X,X) is compact and closed, then it has a fixed point.

As applications of this fixed point theorem, we also get
some coincidence theorems on almost convex sets, which generalize many well-known results.

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