WIAS Preprint No. 1308, (2008)

Uniform boundedness of norms of convex and nonconvex processes


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Seeger, Alberto

2010 Mathematics Subject Classification

  • 34A60 47H04 52A20


  • Convex processes, positively homogeneous maps, controllability, Painleve-Kuratowski limits, graph-convergence




The lower limit of a sequence of closed convex processes is again a closed convex process. In this note we prove the following uniform boundedness principle: if the lower limit is nonempty-valued everywhere, then, starting from a certain index, the given sequence is uniformly norm-bounded. As shown with an example, the uniform boundedness principle is not true if one drops convexity. By way of illustration, we consider an application to the controllability analysis of differential inclusions.

Appeared in

  • Numer. Funct. Anal. Optim., 29 (2008) pp. 551--573.

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