The Locality Property for Compensated Convex Transforms
Journal of convex analysis, Tome 29 (2022) no. 4, pp. 1037-1064
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 Cα, C1,β. We also establish some localised versions of such locality property.
Classification :
52A41, 65K10, 26B25, 14J17
Mots-clés : Convex functions, convex envelope, compensated convex transforms, bounded functions, Cα-functions, C1,β-functions, locality property, density property
Mots-clés : Convex functions, convex envelope, compensated convex transforms, bounded functions, Cα-functions, C1,β-functions, locality property, density property
@article{JCA_2022_29_4_JCA_2022_29_4_a4,
author = {M. S. Alatawi},
title = {The {Locality} {Property} for {Compensated} {Convex} {Transforms}},
journal = {Journal of convex analysis},
pages = {1037--1064},
year = {2022},
volume = {29},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_4_JCA_2022_29_4_a4/}
}
M. S. Alatawi. The Locality Property for Compensated Convex Transforms. Journal of convex analysis, Tome 29 (2022) no. 4, pp. 1037-1064. http://geodesic.mathdoc.fr/item/JCA_2022_29_4_JCA_2022_29_4_a4/