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Vietnam Journal of Mathematics

, Volume 46, Issue 2, pp 391–405 | Cite as

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

  • A. Hantoute
  • A. Jourani
Article
  • 134 Downloads

Abstract

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.

Keywords

Integral sums Convex normal integrands ε-subdifferential Subdifferential calculus 

Mathematics Subject Classification (2010)

26B05 26J25 49H05 

Notes

Acknowledgements

We are very grateful to an anonymous referee for his/her suggestions and comments.

Funding Information

This work is partially supported by CONICYT grant Fondecyt 1151003, Conicyt-Redes no. 150040, and Mathamsud 17-MATH-06.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Centro de Modelamiento Matemático (UMI 2807 CNRS)Universidad de ChileSantiagoChile
  2. 2.Institut de Mathématiques de Bourgogne, UMR 5584 CNRSUniversité de Bourgogne Franche-ComtéDijon CédexFrance

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