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The multidirectional mean value theorem in Banach spaces |
Canad. Math. Bull. 40(1997), 88-102
Published:1997-03-01
Printed: Mar 1997
Printed: Mar 1997
- M. L. Radulescu
- F. H. Clarke
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] |