Abstract

We establish the locality property for compensated convex transforms to functions under various continuity and smoothness. More precisely, we generalise the locality property and the density property for compensated convex transforms obtained recently by K. Zhang, A. Orlando and E. Crooks [Compensated convexity and Hausdorff stable geometric singularity extractions, Math. Models Methods Appl. Sci. 25/4 (2015) 747–801] for bounded functions to functions under various continuity and smoothness assumptions such as CαC^\alpha, C1,βC^{1,\beta}. We also establish some localised versions of such locality property.

Author information

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

Maryam Salem Alatawi

Department of Mathematics, University of Tabuk, Saudi Arabia

msoalatawi@ut.edu.sa

Keywords

  • Convex functions
  • convex envelope
  • compensated convex transforms
  • bounded functions
  • Cα-functions
  • C1
  • β-functions
  • locality property
  • density property

Mathematics Subject Classification

52A41, 65K10, 26B25, 14J17

References

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Suggested citation

M. S. Alatawi. “The Locality Property for Compensated Convex Transforms.” Journal of Convex Analysis 29 (2022), No. 4, 1037–1064. https://doi.org/10.68381/jca29059

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