Uniform boundedness of norms of convex and nonconvex processes
- Henrion, René
- 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.
- Numer. Funct. Anal. Optim., 29 (2008) pp. 551--573.