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 α-monotonicity, where α is the corresponding curve. We study several theoretical properties of α-monotonicity and relate it to other notions of monotonicity, such as weak monotonicity and directional monotonicity.This work is supported by the research group FQM268 of Junta de Andalucía, by the projects TIN2017-89517-P and TIN2016-77356-P (AEI/FEDER, UE), by the the Slovak Scientic Grant Agency VEGA no. 1/0093/17 Identication of risk factors and their impact on products of the insurance and savings schemes, by Slovak grant APVV- 14-0013, and by Czech Project LQ1602 \IT4Innovations excellence in science