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The multidirectional mean value theorem in Banach spaces

Open Access article
 Printed: Mar 1997
  • M. L. Radulescu
  • F. H. Clarke
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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, 49J52 show english descriptions Continuity and differentiation questions
Nonsmooth analysis [See also 46G05, 58C50, 90C56]
26B05 - Continuity and differentiation questions
49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56]

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