Abstract convexity of extended real-valued ICR functions

Abstract

The theory of non-negative increasing and co-radiant (ICR) functions defined on ordered topological vector spaces has been well developed. In this article, we present the theory of extended real-valued ICR functions defined on an ordered topological vector space X. We first give a characterization for non-positive ICR functions and examine abstract convexity of this class of functions. We also investigate polar function and subdifferential of these functions. Finally, we characterize abstract convexity, support set and subdifferential of extended real-valued ICR functions.

Keywords:

• monotonic analysis
• ICR function
• subdifferential
• support set
• co-radiant set
• radiant set
• abstract convexity

AMS Subject Classifications::

• 26B25
• 26A48

Acknowledgements

The authors are very grateful to the anonymous referees for their useful suggestions on an earlier version of this article. These suggestions have enabled the authors to improve the article significantly. This research was supported partially by Kerman Graduate University of Technology and Mahani Mathematical Research Center.