On Commuting Functions.
It is a rather well-known conjecture that, if f and g are continuous functions which commute (i.e., f(g(x)) = g(f(x))), then f and g have a common fixed point. The conjecture is known to be true in some special cases; e.g., when f and g are polynomials. H. Cohen has proved the conjecture for the case when f and g have a property he calls fullness. This Memorandum generalizes Cohen's theorem to the case when f is full and g is arbitrary