Geodesic
MVT, Integration, and Monotonicity of a Generalized Subdifferential in Locally Convex Spaces
Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1345-1362
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We extend Zagrodny's Mean Value Theorem (MVT) to the class of weakly lower semicontinuous epi-pointed functions defined in locally convex spaces. With this at hand we extend the integration of generalized subdifferentials and the characterization of convexity via the monotonicity of the subdifferential.
Classification : 49J53, 49J52
Mots-clés : Approximate Mean Value Theorem, integration of subdifferentials, monotonicity of the subdifferential, epi-pointed functions, generalized subdifferentials 
@article{JCA_2020_27_4_JCA_2020_27_4_a14,
     author = {R. Correa and A. Hantoute and P. P\'erez-Aros},
     title = {MVT, {Integration,} and {Monotonicity} of a {Generalized} {Subdifferential} in {Locally} {Convex} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1345--1362},
     year = {2020},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a14/}
}
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R. Correa; A. Hantoute; P. Pérez-Aros. MVT, Integration, and Monotonicity of a Generalized Subdifferential in Locally Convex Spaces. Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1345-1362. http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a14/