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- Title
Generalized positive sets and abstract monotonicity.
- Authors
Mohebi, H.; Sattarzadeh, A.
- Abstract
The theory of q-positive sets on SSD spaces has been introduced by Simons (J Convex Anal, 14:297-317, ; From Hahn-Banach to monotonicity, Springer, Berlin, ). 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.
- Subjects
BANACH spaces; FRACTIONAL calculus; POSITIVE operators; MONOTONIC functions; CONVEX functions; HAHN-Banach theorem
- Publication
Positivity, 2013, Vol 17, Issue 3, p601
- ISSN
1385-1292
- Publication type
Article
- DOI
10.1007/s11117-012-0192-6