Journal of Convex Analysis 15 (2008), No. 3, 561--579
Copyright Heldermann Verlag 2008
Monotonic Analysis over Cones: III
Joydeep Dutta
Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016 Kanpur, India
jdutta@iitk.ac.in
Juan Enrique Martínez-Legaz
Dep. d'Economia i d'Història Economica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
JuanEnrique.Martinez@uab.es
Alex M. Rubinov
CIAO -- SITMS, University of Ballarat, P.O. Box 663, Ballarat, Vic. 3353, Australia
[Parts I and II of this article were published in Optimization 53 (2004) 165--177 and 529--547.]
This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.
Keywords: Monotonic analysis, ICR functions, abstract convexity, radiant sets, co-radiant sets, normal sets, co-normal sets.
MSC: 26B25, 26A48
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