Description and Properties of Curve-Based Monotone Functions.

Curve-based monotonicity is one of the lately introduced relaxations of monotonicity. As directional monotonicity regards monotonicity along fixed rays, which are given by real vectors, curve-based monotonicity studies the increase of functions with respect to a general curve a. In this work we study some theoretical properties of this type of monotonicity and we relate this concept with previous relaxations of monotonicity.