# MR2817222 Ursescu, Corneliu, A mean value inequality formultifunctions. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 54(102)(2011), no. 2, 193–200

Risultato della ricerca: Review articlepeer review

## Abstract

The paper is devoted to extend some mean value inequalities from thefunction setting to the multifunction one. Let (M,d) be a metric space, let F be a multifunctions defined on D \subset R and takingvalues in the family of nonempty subsets of M, and let g: D\rightarrowR be a strictly increasing function. The author proves thefollowing inequality:\frac{\delta(F(b),F(a))}{g(b)-g(a)} \leq \sup_{s\in [a,b)\cap D}\sup_{S\in F(s)}\sup_{t\in (s,b)\cap D} \frac{\delta(F(t),S)}{g(t)-g(s)}, where a and b are two points of D with a<b and, if Qand P are nonempty subsets of M, then \delta(Q,P)=\sup_{p\in P} \inf_{q\in Q}d(q,p).An application of the previous inequality to the Dini derivativesof a multifunction is also given.Reviewed by L. Di Piazza
Lingua originale English 1 MATHEMATICAL REVIEWS MR2817222 Published - 2011