• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.11-20
• /
• 2008

We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class $\cal{B}$ of maps. We also give 16 conjectures related to that theory.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.885-899
• /
• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Journal of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.1-27
• /
• 2008

We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.