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Journal of Convex Analysis 27 (2020), No. 4, 1345--1362
Copyright Heldermann Verlag 2020

MVT, Integration, and Monotonicity of a Generalized Subdifferential in Locally Convex Spaces

Rafael Correa
Universidad de O'Higgins, and: DIM-CMM, Universidad de Chile, Chile

Abderrahim Hantoute
Center for Mathematical Modeling, Universidad de Chile, Chile
and: Department of Mathematics, University of Alicante, Alicante, Spain

Pedro Pérez-Aros
Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Chile

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.

Keywords: Approximate Mean Value Theorem, integration of subdifferentials, monotonicity of the subdifferential, epi-pointed functions, generalized subdifferentials.

MSC: 49J53, 49J52.

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