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. In this work we study some theoretical properties of this type of monotonicity and we relate this concept with previous relaxations of monotonicity.This work is supported by the research group FQM268 of Junta de Andalucía, by the project TIN2016-77356-P (AEI/FEDER, UE), by the Slovak Scientific Grant Agency VEGA no. 1/0093/17 Identification 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'