Hiriart-Urruty–Phelps-Like Formula for the Subdifferential of Integral Sums

Abderrahim Hantoute (1) , Abderrahim Jourani (2)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We provide subdifferential calculus rules for continuous sums parametrized in measurable spaces that use the approximate subdifferentials of the data functions. As in Hiriart-Urruty and Phelps (J. Funct. Anal. 118: 154–166, 1993) given for finite sums, the resulting formulas hold without any conditions of continuity type on the involved functions. All this analysis is done in the setting of locally convex Suslin spaces.

Mots clés: Integral sums; Convex normal integrands; ε-subdifferential; Subdifferential calculus

Domaines: Mathématiques [math]

Abderrahim Hantoute, Abderrahim Jourani. Hiriart-Urruty–Phelps-Like Formula for the Subdifferential of Integral Sums. Vietnam Journal of Mathematics, 2018, 46 (2), pp.391-405. ⟨10.1007/s10013-018-0291-1⟩. ⟨hal-01801657⟩