Strongly convex set-valued maps

Hugo Leiva (), Nelson Merentes (), Kazimierz Nikodem () and José Sánchez ()

Journal of Global Optimization, 2013, vol. 57, issue 3, 695-705

Abstract: We introduce the notion of strongly $$t$$ -convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly $$t$$ -convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representation is given. Finally, a connection between strongly convex set-valued maps and strongly convex sets is presented. Copyright The Author(s) 2013

Keywords: Strongly convex function; Strongly convex set-valued map; Strongly convex set; Primary 26B25; Secondary 54C60; 46C15; 39B62 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-013-0051-4

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