Geodesic
A General Result About Inner Regularization of Sets
Journal of convex analysis, Tome 27 (2020) no. 3, pp. 943-958
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We generalize a recent result of C. Nour, H. Saoud and J. Takche [Regularization via sets satisfying the interior sphere condition, J. Convex Analysis 25(1) (2018) 1--19], where the authors provided an inner approximation of a subset S of the n-dimensional real space Rn by sets satisfying the interior sphere condition. The main idea is to replace the convex cones used there by curved ones which leads us to weaken the assumptions and cover more sets S.
Classification : 35J20, 35J62, 35P30
Mots-clés : Interior sphere condition, union of closed balls property, phi-convexity, proximal smoothness, S-convexity, proximal analysis, nonsmooth analysis 
@article{JCA_2020_27_3_JCA_2020_27_3_a8,
     author = {C. Nour and J. Takche},
     title = {A {General} {Result} {About} {Inner} {Regularization} of {Sets}},
     journal = {Journal of convex analysis},
     pages = {943--958},
     year = {2020},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a8/}
}
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C. Nour; J. Takche. A General Result About Inner Regularization of Sets. Journal of convex analysis, Tome 27 (2020) no. 3, pp. 943-958. http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a8/