Quasimonotonicity

We consider functions in ordered Banach spaces which are quasimonotone incr easing (in the sense of Volkmann). The definition of quasimonotonicity orig inated from the search for a general frame for results on differential ineq ualities. Meanwhile such functions are involved in several parts of nonline ar analysis such as the qualitative and quantitative behaviour of dynamical systems or fixed point theory. This paper is a survey on some recent aspec ts on quasimonotone increasing functions.