Continuous Selections in ${\alpha }$-Convex Metric Spaces

Volume 52 / 2004

F. S. De Blasi, G. Pianigiani Bulletin Polish Acad. Sci. Math. 52 (2004), 303-317 MSC: Primary 54C65; Secondary 54C60. DOI: 10.4064/ba52-3-10


The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered $n$-tuple of points.


  • F. S. De BlasiCentro Vito Volterra
    Dipartimento di Matematica
    Università di Roma II (Tor Vergata)
    Via della Ricerca Scientifica
    00133 Roma, Italy
  • G. PianigianiDipartimento di Matematica per le Decisioni
    Università di Firenze
    Via Lombroso, 6/17
    50134 Firenze, Italy

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