General theorems of the Knaster-Kuratowski- Mazurkiewicz type and applications to the existence study in optimization
Phan Quốc Khánh, Vo Si Trong Long · Optimization · 2020
We establish theorems of the Knaster-Kuratowski-Mazurkiewicz (KKM) type on topological spaces with topologically-based generalized convex structures and apply them to the existence study for variational relation problems, variational inequalities, minimax inequalities and saddle points, and to alternative theorems. Our first main KKM-type theorem is a necessary and sufficient condition, not only a sufficient one as usual. The results improve and extend corresponding contributions in the literature in many aspects.