Abstract

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\varphi_0-convexity, θ0\theta_0-exterior sphere condition, and ψ0\psi_0-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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • S-convexity
  • phi-convexity
  • theta-exterior sphere condition
  • psi-union of closed balls property
  • proximal analysis
  • nonsmooth analysis

Mathematics Subject Classification

49J52, 52A20, 93B27

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Suggested citation

C. Nour, J. Takche. “S-Convexity: The Variable Radius Case.” Journal of Convex Analysis 29 (2022), No. 4, 1167–1192. https://doi.org/10.68381/jca29065

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.