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The Multidirectional Mean Value Theorem in Banach Spaces

Published online by Cambridge University Press:  20 November 2018

M. L. Radulescu  and
F. H. Clarke
M. L. Radulescu
Affiliation:
Centre de recherches mathématiques Université de Montréal C.P. 6128, Succ. Centre-ville Montréal, Québec H3C 3J7
F. H. Clarke
Affiliation:
Centre de recherches mathématiques Université de Montréal C.P. 6128, Succ. Centre-ville Montréal, Québec H3C 3J7
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Abstract

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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 C1-Lipschitz continuous bump function.

Keywords

26B0549J52
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 1 , 01 March 1997 , pp. 88 - 102
Copyright
Copyright © Canadian Mathematical Society 1997

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