Recently, Borwein and Moors (1998) introduced a new class of tangentially regular sets in IRn (called arc-wise essentially smooth sets). They characterized the sets S of this class in terms of arc-wise essential smoothness of the distance function dS. Very recently, the author (2002) gave an appropriate extension of this class to any Banach space X and he extended the above characterization to any Banach space X with a uniformly Gˆateaux differentiable norm. In this paper we extend the concept of arc-wise essentially smooth sets to set-valued mappings C : [0, T]⇉X (T > 0) and we will use this concept to establish an important application to nonconvex sweeping process.
@article{1526,
title = {Arc-wise Essentially Tangentially Regular Set-valued Mappings and their Applications to Nonconvex Sweeping Process},
journal = {CUBO, A Mathematical Journal},
volume = {10},
year = {2008},
language = {en},
url = {http://dml.mathdoc.fr/item/1526}
}
Bounkhel, Messaoud. Arc-wise Essentially Tangentially Regular Set-valued Mappings and their Applications to Nonconvex Sweeping Process. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1526/