## Minimax inequality of Ky Fan type in $$H$$-spaces with applications.(English)Zbl 0948.47049

Summary: We prove a main result about the Ky Fan minimax inequality in any compact $$H$$-space. Then, we apply this result to fixed point problem, intersection problem of sets with convex sections, minimax inequality of the von Neumann type, and variational inequality.

### MSC:

 47H04 Set-valued operators 47J20 Variational and other types of inequalities involving nonlinear operators (general) 47H10 Fixed-point theorems 49J35 Existence of solutions for minimax problems 52A07 Convex sets in topological vector spaces (aspects of convex geometry)
Full Text: