Mathematica Eterna
Open Access

Abstract

Strongly concave set-valued maps

Odalis Mej´ıa, Nelson Merentes and Kazimierz Nikodem

The notion of strongly concave set-valued maps is introduced and some properties of it are presented. In particular, a Kuhn-type result as well as Bernstein-Doetsch and Sierpi´nski-type theorems for strongly midconcave set-valued maps are obtained. A representation of strongly concave set-valued maps in inner product spaces is given.