Approximate selections in ${\alpha}$-convex metric spaces and topological degree

Francesco S. de Blasi, Giulio Pianigiani

DOI: http://dx.doi.org/10.12775/TMNA.2004.032

Abstract


The existence of continuous approximate selections is proved for a class
of upper semicontinuous multifunctions taking closed $\alpha$-convex
values in a metric space equipped with an appropriate notion
of $\alpha$-convexity.
The approach is based on the definition of pseudo-barycenter of an ordered
$n$-tuple of points.
As an application, a notion of topological degree for a class of $\alpha$-convex
multifunctions is developed.

Keywords


Continuous approximate selection; multifunction; convex metric space; pseudo-barycenter; topological degree

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