A Clarke-Ledyaev type inequality for certain non-convex sets (Q2752991)

The question whether the assumption of convexity of the set involved in the Clarke-Ledyaev inequality can be relaxed is studied. A geometrical relation between a point and a set, that ``the set seems convex from a point outside its convex hull'', is introduced in the paper. A Clarke-Ledyaev type inequality is proved if the point and the set satisfy this geometrical relation. It is also shown that if this relation is not present, the considered type of inequality may not hold.