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Strongly convex set-valued maps

Author

Listed:
  • Hugo Leiva
  • Nelson Merentes
  • Kazimierz Nikodem
  • José Sánchez

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

Suggested Citation

  • Hugo Leiva & Nelson Merentes & Kazimierz Nikodem & José Sánchez, 2013. "Strongly convex set-valued maps," Journal of Global Optimization, Springer, vol. 57(3), pages 695-705, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:695-705
    DOI: 10.1007/s10898-013-0051-4
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    References listed on IDEAS

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