Geodesic
Continuous Selections in ${\alpha }$-Convex Metric Spaces
F. S. De Blasi1 ; G. Pianigiani2
1 Centro Vito Volterra Dipartimento di Matematica Università di Roma II (Tor Vergata) Via della Ricerca Scientifica 00133 Roma, Italy
2 Dipartimento di Matematica per le Decisioni Università di Firenze Via Lombroso, 6/17 50134 Firenze, Italy
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 303-317 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba52-3-10
Keywords: existence continuous selections proved class lower semicontinuous multifunctions whose values closed convex subsets complete metric space equipped appropriate notion convexity approach based notion pseudo barycenter ordered n tuple points

F. S. De Blasi 1 ; G. Pianigiani 2

1 Centro Vito Volterra Dipartimento di Matematica Università di Roma II (Tor Vergata) Via della Ricerca Scientifica 00133 Roma, Italy
2 Dipartimento di Matematica per le Decisioni Università di Firenze Via Lombroso, 6/17 50134 Firenze, Italy 
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     author = {F. S. De Blasi and G. Pianigiani},
     title = {Continuous {Selections} in ${\alpha }${-Convex} {Metric} {Spaces}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {303--317},
     year = {2004},
     volume = {52},
     number = {3},
     doi = {10.4064/ba52-3-10},
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F. S. De Blasi; G. Pianigiani. Continuous Selections in ${\alpha }$-Convex Metric Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 303-317. doi: 10.4064/ba52-3-10

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