Abstract
The theory of q-positive sets on SSD spaces has been introduced by Simons (J Convex Anal, 14:297–317, 2007; From Hahn–Banach to monotonicity, Springer, Berlin, 2008). Monotone sets can be considered as special case of q-positive sets. In this paper, we develop a theory of q-positive sets in the framework of abstract monotonicity. We use generalized Fenchel’s duality theorem and give some criteria for maximality of abstract q-positive sets. Finally, we investigate the relation between abstract q-positive sets and abstract convex functions.
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Mohebi, H., Sattarzadeh, A.R. Generalized positive sets and abstract monotonicity. Positivity 17, 601–620 (2013). https://doi.org/10.1007/s11117-012-0192-6
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DOI: https://doi.org/10.1007/s11117-012-0192-6
Keywords
- Generalized Fenchel’s duality
- q-Positive set
- Abstract monotonicity
- Abstract convexity
- Abstract convex function