A Chain Rule for Upper Semicontinuous (CF)-Mappings

A chain rule for calculating convexificators of composite functions of the type f  =  h∘g, with the inner factor g being a transformation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^n$$\end{document}, is proposed. The proof is based on a double application of a mean value theorem for (CF)-mappings due to V.F. Demyanov and V. Jeyakumar (see [4]), along with a stability property for the support of a certain ɛ-perturbation of (CF)-mappings.