Approximations and continuous selections of multifunctions in convex metric spaces
by
Francesco Saverio de Blasi
University of Roma ``Tor Vergata''
Coauthors: Giulio Pianigiani (University of Florence)

In non linear spaces in absence of a natural notion of a convex set, different approaches to convexity have been developed so far. The one considered here is in the spirit of some ideas which go back to Stone, Michael, Takahashi. In normed spaces barycenters play a fundamental role in approximation and selection problems for multifunctions, when partition of unity techniques are employed. In metric spaces an analogous notion will be considered, that of pseudo-barycenter. This retains only a few properties of the barycenter, yet it turns out to be useful in continuous approximation and selection problems. Some applications are discussed as well.

Date received: July 16, 2001