Abstract

We establish a class of multifunctions having smooth (C∞C^\infty) selections and formulate assumptions on a multifunction FF under which for any continuous selection ff of FF there is a sequence of smooth selections of FF converging uniformly to ff. Moreover, we obtain a Castaing type representation of multifunctions by a sequence of smooth selections, i.e. we construct a sequence {fk}\{f_k\} of smooth selections of FF satisfying the condition F(x)=∪k≥1 fk(x)‾F(x)=\overline{\cup_{k\geq 1} \ f_k(x)} for all x∈Xx\in X.

Author information

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Jacek Sadowski

Faculty of Mathematics, Politechnika Warszawska, ul. Koszykowa 75, 00-662 Warszawa, Poland

j.sadowski@mini.pw.edu.pl

Keywords

  • Lower semicontinuous multifunction
  • smooth selection
  • uniform convergence
  • approximation
  • convolution
  • Castaing representation

Mathematics Subject Classification

26E25, 54C60, 54C65

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Suggested citation

J. Sadowski. “Smooth Selections of Convex-Valued Multifunctions.” Journal of Convex Analysis 20 (2013), No. 1, 25–42. https://doi.org/10.68381/jca20003

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.