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We consider the question whether the assumption of convexity
of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case
when the point is outside the convex hull of the set we show that Clarke-Ledyaev
type inequality holds if and only if there is certain geometrical relation between the point and the set.
We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.
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