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Search: MSC category 49J52 ( Nonsmooth analysis [See also 46G05, 58C50, 90C56] )

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1. CMB 2005 (vol 48 pp. 283)

Thibault, Lionel; Zagrodny, Dariusz
 Enlarged Inclusion of Subdifferentials This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions $f$ and $g$ have the subdifferential of $f$ included in the $\gamma$-enlargement of the subdifferential of $g$, then the difference of those functions is $\gamma$-Lipschitz over their effective domain. Keywords:subdifferential,, directionally regular function,, approximate convex function,, subdifferentially and directionally stable functionCategories:49J52, 46N10, 58C20

2. CMB 2000 (vol 43 pp. 25)

Bounkhel, M.; Thibault, L.
 Subdifferential Regularity of Directionally Lipschitzian Functions Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established. Keywords:subdifferential regularity, directional regularity, directionally Lipschitzian functionsCategories:49J52, 58C20, 49J50, 90C26

3. CMB 1998 (vol 41 pp. 497)

Borwein, J. M.; Girgensohn, R.; Wang, Xianfu
 On the construction of HÃ¶lder and Proximal Subderivatives We construct Lipschitz functions such that for all $s>0$ they are $s$-H\"older, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed H\"older and approximate subderivatives. Keywords:Lipschitz functions, HÃ¶lder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, HÃ¶lder smooth, dyadic rationalsCategories:49J52, 26A16, 26A24

4. CMB 1998 (vol 41 pp. 41)

Giner, E.
 On the Clarke subdifferential of an integral functional on $L_p$, $1\leq p < \infty$ Given an integral functional defined on $L_p$, $1 \leq p <\infty$, under a growth condition we give an upper bound of the Clarke directional derivative and we obtain a nice inclusion between the Clarke subdifferential of the integral functional and the set of selections of the subdifferential of the integrand. Keywords:Integral functional, integrand, epi-derivativeCategories:28A25, 49J52, 46E30

5. CMB 1997 (vol 40 pp. 88)

Radulescu, M. L.; Clarke, F. H.
 The multidirectional mean value theorem in Banach spaces 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. Categories:26B05, 49J52
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