Commuting Functions with No Common Fixed Point
Commuting Functions with No Common Fixed Point
Introduction.Let/and g be continuous functions mapping the unit interval / into itself which commute under functional composition, that is, f(g(x)) = g(f(x)) for all x in /.In 1954 Eldon Dyer asked whether/and g must always have a common fixed point, meaning a point z in / for which f(z) = …