Weakly \(G\)-KKM mappings, \(G\)-KKM property, and minimax inequalities (Q596711)

The author extends the concept of generalized \(G\)-KKM mappings, given by Lin, Ko and Park in the setting of \(G\)-convex spaces, introducing the new concept of a weakly \(G\)-KMM mapping. Exploiting this new definition, the author states two intersection results, and, as a consequence, a minimax theorem, with some variants of it. In the last section, conditions for a map to have the \(G\)-KKM property are given, and a Sion type minimax inequality is proved.