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We state a necessary and sufficient polyconvexity condition inR2X2for functions of classC1. This condition is applied tof(X) = |X|2(|X|2−2 detX) for obtaining a convex representation inR2X2xR.

The paper deals with several kinds of roughly. globally and ?;-convex functions on the real line. In particular, an interesting property of roughly convex functions in the sense of Klotzler (it suffices to consider points with a distance equal to the roughness degree) is verified, a sharpened y-convexity condition (which is satisfied by Favard's "fonction penetrante") is introduced. and some continuous counterexamples are given.

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