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Mean-Value Theorem with Small Subdifferentials

J. P. Penot
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J. P. Penot: University of Pau

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 1, No 13, 209-221

Abstract: Abstract We prove a mean-value theorem for lower semicontinuous functions on a large class of Banach spaces which contains the class of Asplund spaces, in particular reflexive Banach spaces and Banach spaces with a separable dual. It involves the lower subdifferential (or contingent subdifferential) and the Fréchet subdifferentials, which are among the smallest subdifferentials known to date. It follows that the estimates which it provides require weak assumptions and are accurate. When the function is locally Lipschitzian, we get a simple statement which refines the Lebourg mean-value theorem.

Keywords: Fuzzy calculus; generalized derivatives; mean-value theorem; nonsmooth analysis; subdifferentials (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022672005994

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