A+ CATEGORY SCIENTIFIC UNIT

On convex and $*$-concave multifunctions

Volume 86 / 2005

Bożena Pi/atek 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 $s,t\in[a,b]$, $s< t$.

Authors

  • Bożena Pi/atekInstitute of Mathematics
    Silesian University of Technology
    Kaszubska 23
    44-100 Gliwice, Poland
    e-mail

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