On convex and $*$-concave multifunctions
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 165-170
MSC: 39B62, 26E25.
DOI: 10.4064/ap86-2-6
Abstract
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 $s,t\in[a,b]$, $s< t$.
