GENERALIZATIONS OF THE KKMF PRINCIPLE HAVING COERCING FAMILIES
In 2005 , Ben-El-Mechaiekh, Chebbi, and Florenzanoobtained a generalization of the Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also obtained a Fan-Browder type fixed point theorem to a set-valued map on non-compact convex sets. In 2011 , Chebbi, Gourdel, and Hammami introduced a generalized coercivity type condition for set-valued maps defined on topological spaces endowed with a generalized convex structure and extendedFan's KKM theorem. In this paper, we show that better forms of theorems in  and  can be deduced from a KKM theorem on abstract convex spaces in Park's sense [11-15].
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