Journal of Convex Analysis 29 (2022), No. 4, 1167--1192
Copyright Heldermann Verlag 2022
S-Convexity: The Variable Radius Case
Chadi Nour
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon
cnour@lau.edu.lb
Jean Takche
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon
jtakchi@lau.edu.lb
We generalize, to the variable radius case, the main results contained in a recent paper of the authors [A new class of sets regularity, J. Convex Analysis 25/4 (2018) 1059--1074], where a new regularity class, called S-convexity, is studied and shown to cover well-known regularity properties, including ϕ0-convexity, θ0-exterior sphere condition, and &psi0-union of closed balls property. Furthermore, we provide using S-convexity, new additional characterizations of the variable and the constant radius form of these three regularity properties.
Keywords: S-convexity, phi-convexity, theta-exterior sphere condition, psi-union of closed balls property, proximal analysis, nonsmooth analysis.
MSC: 49J52, 52A20, 93B27.
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