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The multidirectional mean value theorem in Banach spaces

Published:1997-03-01
Printed: Mar 1997
• M. L. Radulescu
• F. H. Clarke
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Abstract

Recently, F.~H.~Clarke and Y.~Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certain Banach spaces, namely those that admit a ${\cal C}^1$-Lipschitz continuous bump function.
 MSC Classifications: 26B05 - Continuity and differentiation questions 49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56]

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