Geodesic
On convex and $*$-concave multifunctions
Bożena Pi/atek1
1 Institute of Mathematics Silesian University of Technology Kaszubska 23 44-100 Gliwice, Poland
Annales Polonici Mathematici, Tome 86 (2005) no. 2, pp. 165-170 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A continuous multifunction $F:[a,b]\to {\rm clb}(Y)$ is $*$-concave if and only if the inclusion $$ \frac{1}{t-s}\int_s^t F(x)\,dx \subset \frac{F(s) \mathbin{\buildrel{\ast}\over{+}} F(t)}{2} $$ holds for every $s,t\in[a,b]$, $s t$.
DOI : 10.4064/ap86-2-6
Keywords: continuous multifunction clb * concave only inclusion frac t s int x subset frac mathbin buildrel ast holds every

Bożena Pi/atek 1

1 Institute of Mathematics Silesian University of Technology Kaszubska 23 44-100 Gliwice, Poland 
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Bożena Pi/atek. On convex and $*$-concave multifunctions. Annales Polonici Mathematici, Tome 86 (2005) no. 2, pp. 165-170. doi: 10.4064/ap86-2-6

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