A remark on Clarke's tangent cone (Q1087818)

Consider a multivalued mapping F from a normed space X into another Y, and denote by \(T_{\Omega}(z_ 0)\) the Clarke's tangent cone to the set \(\Omega =graph\) F at \(z_ 0=(x_ 0,x_ 0)\in \Omega\). The aim of this paper is to describe a relation between the cone \(T_{\Omega}(z_ 0)\) and the set \(F(x_ 0)\). Namely we shall establish the following equality: \[ T_{F(x_ 0)}(y_ 0)=\{y: (0,y)\in T_{\Omega}(z_ 0)\}. \]