Abstract convexity of topical functions

H. Mohebi () and M. Samet ()

Journal of Global Optimization, 2014, vol. 58, issue 2, 365-375

Abstract: In this paper, we examine properties of topical (increasing and plus-homogeneous) functions defined on a normed linear space $${X}$$ . We also study many results of abstract convexity such as support set, polarity and subdifferential set of these functions. Finally, we give a characterization for topical functions with respect to closed downward sets. Copyright Springer Science+Business Media New York 2014

Keywords: Monotonic analysis; Topical function; Downward set; Upward set; Abstract convexity; Primary: 26B25; 52A41; Secondary: 46B42 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-013-0037-2

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