Subdifferential and properties of convex functions with respect to vector fields

@inproceedings{Bardi2014SubdifferentialAP,
  title={Subdifferential and properties of convex functions with respect to vector fields},
  author={Martino Bardi and Federica Dragoni},
  year={2014}
}
We study properties of functions convex with respect to a given family X of vector fields, a notion that appears natural in Carnot-Carath eodory metric spaces. We define a suitable sub- differential and show that a continuous function is X -convex if and only if such subdifferential is nonempty at every point. For vector fields of Carnot type we deduce from this property that a generalized Fenchel transform is involutive and a weak form of Jensen inequality. Finally we introduce and compare… CONTINUE READING

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