A -map of a closed interval into itself is called an -map if it has a unique critical point such that for , for , and for all . The authors establish a dichotomy result for -maps with negative Schwarzian derivative which is then applied to several classes of functional differential equations including Wright and Mackey-Glass delay differential equations. In particular, easily computable bounds for the global attractor of a delay differential equation
where and is a continuous function, are obtained. This nice paper concludes with an interesting conjecture for (1), a discussion of related results and open problems.