Journal of Convex Analysis 27 (2020), No. 3, 943--958
Copyright Heldermann Verlag 2020
A General Result About Inner Regularization of Sets
Chadi Nour
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
cnour@lau.edu.lb
Jean Takche
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
jtakchi@lau.edu.lb
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.
Keywords: Interior sphere condition, union of closed balls property, phi-convexity, proximal smoothness, S-convexity, proximal analysis, nonsmooth analysis.
MSC: 35J20, 35J62, 35P30.
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