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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

Juan Enrique MartŪnez-Legaz
Dep. d'Economia i d'HistÚria Economica, Universitat AutÚnoma de Barcelona, 08193 Bellaterra, Spain

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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