Abstract

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\mathbb{R}^n 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.

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, Lebanon

cnour@lau.edu.lb

Jean Takche

Dept. of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

jtakchi@lau.edu.lb

Keywords

  • Interior sphere condition
  • union of closed balls property
  • phi-convexity
  • proximal smoothness
  • S-convexity
  • proximal analysis
  • nonsmooth analysis

Mathematics Subject Classification

35J20, 35J62, 35P30

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Suggested citation

C. Nour, J. Takche. “A General Result About Inner Regularization of Sets.” Journal of Convex Analysis 27 (2020), No. 3, 943–958. https://doi.org/10.68381/jca27048

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.