Abstract: Some new weak Knaster-Kuratouski-Mazurkiewicz (KKM) theorems are proved under the noncompact situation in the generalized finitely continuous space (GFCspace) without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.

Key words: non-linear, stochastic, recursive, wavelet transform, weak Knaster-Kuratouski-Mazurkiewicz (KKM) mapping, generalized finitely continuous space (GFC-space), minimax inequality, GFC-quasicovex