Characterizations of convex approximate subdifferential calculus in Banach spaces

Correa, R.; Hantoute, A.; Jourani, A.

doi:10.1090/tran/6589

Characterizations of convex approximate subdifferential calculus in Banach spaces
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by R. Correa, A. Hantoute and A. Jourani PDF

Trans. Amer. Math. Soc. 368 (2016), 4831-4854 Request permission

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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