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Positivity

, Volume 17, Issue 3, pp 601–620 | Cite as

Generalized positive sets and abstract monotonicity

  • H. Mohebi
  • A. R. Sattarzadeh
Article

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.

Keywords

Generalized Fenchel’s duality q-Positive set Abstract monotonicity Abstract convexity Abstract convex function 

Mathematics Subject Classification (2000)

47H05 47H04 52A01 26A51 26B25 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsShahid Bahonar University of Kerman and Kerman Graduate University of TechnologyKermanIran

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