Characterizations of convex approximate subdifferential calculus in Banach spaces

Abstract : We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.
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https://hal.archives-ouvertes.fr/hal-01414713
Contributor : Imb - Université de Bourgogne <>
Submitted on : Monday, December 12, 2016 - 3:03:38 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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Rafael Correa, Abderrahim Hantoute, Abderrahim Jourani. Characterizations of convex approximate subdifferential calculus in Banach spaces. Transactions of the American Mathematical Society, American Mathematical Society, 2016, 368 (7), pp.4831 - 4854. ⟨10.1090/tran/6589⟩. ⟨hal-01414713⟩

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