Common fixed points for commuting Cournot maps.

Abstract

We study some conditions to guarantee the existence of common fixed points of two commuting Cournot maps $F(x,y)=(f_{2}(y),f_{1}(x)),$ $G(x,y)=(g_{2}(y),g_{1}(x)),$ defined from $I^{2}=[0,1]^{2}$ into itself. In particular, we prove that Jungck's Theorem and Jachymski's equivalent conditions can be only partially proved in this setting.