Generalized minimax inequalities and fixed point theorems (Q1192893)

Ky Fan's minimax inequality plays an important part in variational inequalities, game theory, economic mathematics and optimization. This minimax inequality has been generalized and improved by many researchers. In this inequality, one of the most fundamental conditions, i.e. convexity (concavity) has been weakened to diagonal convexity (concavity). The authors propose more general convexity (concavity) conditions, e.g. \(T\)-diagonal convexity (concavity), and obtain results generalizing and improving previous ones. This allows them to discuss well-known fixed point problems in the light of the above mentioned results such as the famous Fan-Glicksberg theorem.