Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces

Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FC$FC$-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature.