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From relative convexity to modulus of continuity estimates for the dual gradient mapping

Let $F: \mathbf{R}^d \to \mathbf{R}$ be a convex function, let $m > 0$, and define $Q_m: \mathbf{R}^d \to \mathbf{R}$ to be the mapping $x \mapsto \frac{m}{2} \| x \|_2^2$. One says that $F$ is $m$-...