GENERALIZATIONS OF THE KKMF PRINCIPLE HAVING COERCING FAMILIES - Park, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
In 2005 [1], 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 [3], 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 [1] and [3] can be deduced from a KKM theorem on abstract convex spaces in Park’s sense [11-15].