On the differentiability of set-valued functions defined on a Banach space and mean value theorem

摘要

In this paper we introduce a new concept of differentiability for set-valued functions defined from an open set of a Banach space X to the family of all non-empty, bounded closed subsets of a Banach space Y and give some of its properties. We also give two forms of a mean-value theorem for this type of set-valued functions.