KKM Theorems on FC-Spaces with Their Applications to Variational Inequalities (Communications in Mathematical Research, 2021)
A new concept of finitely continuous topological spaces (in short, FC-space) without convexity structure and linear structure was introduced. Some KKM type theorems in noncompact FC-spaces were obtained, and from which, some section theorems and variational inequality theorems were proved under much weak assumptions. Our results improve and generalize the corresponding conclusions in recent literature.
Keywords: FC-space; FC-subspace; KKM map; lower semicontinuous; variational inequality.