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Soit \(f : {\R^{+*}} \to \R\) convexe et \(g : {\R^{+*}} \to \R\) affine. On suppose : \(\begin{cases}\forall\ x > 0,\ f(x) \le g(x),\cr f(1) = g(1).\cr\end{cases}\)
Montrer que \(f = g\).
Soit \(f : {\R^{+*}} \to \R\) convexe et \(g : {\R^{+*}} \to \R\) affine. On suppose : \(\begin{cases}\forall\ x > 0,\ f(x) \le g(x),\cr f(1) = g(1).\cr\end{cases}\)
Montrer que \(f = g\).