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In 1977, Baillon and Haddad proved that if the gradient of a convex and continuously differentiable function is nonexpansive, then it is actually firmly nonexpansive.
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H. Attouch, L. M. Briceño-Arias, and P. L. Combettes: A parallel splitting method for coupled monotone inclusions, SIAM J. Control Optim. to appear
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