Curve-Based Monotonicity: A Generalization Of Directional Monotonicity

In this work we propose a generalization of the notion of directional monotonicity. Instead of considering increasingness or decreasingness along rays, we allow more general paths defined by curves in the n-dimensional space. These considerations lead us to the notion of -monotonicity, where is the corresponding curve. We study several theoretical properties of -monotonicity and relate it to other notions of monotonicity, such as weak monotonicity and directional monotonicity.