- Volume 32 Issue 2
Ky Fan's minimax inequality is an important tool in nonlinear functional analysis and its applications, e.g. game theory and economic theory. Since Fan gave his minimax inequality in , various extensions of this interesting result have been obtained (see [4,11] and the references therein). Using Fan's minimax inequality, Ha  obtained a non-compact version of Sion's minimax theorem in topological vector spaces, and next Geraghty-Lin , Granas-Liu , Shih-Tan , Simons , Lin-Quan , Park-Bae-Kang , Bae-Kim-Tan  further generalize Fan's minimax theorem in more general settings. In , using the concept of submaximum, Komiya proved a topological minimax theorem which also generalized Sion's minimax theorem and another minimax theorem of Ha in  without using linear structures. And next Lin-Quan  further generalizes his result to two function versions and non-compact topological settings.