The regularity property of compensated convex transforms for semiconvex functions of general modulus (Q6620695)
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scientific article; zbMATH DE number 7928039
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The regularity property of compensated convex transforms for semiconvex functions of general modulus |
scientific article; zbMATH DE number 7928039 |
Statements
The regularity property of compensated convex transforms for semiconvex functions of general modulus (English)
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17 October 2024
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A general approximation theorem for semiconvex and semiconcave functions with general modulus is provided by means of compensated convex transforms. In particular, it is shown that the limit of the gradient of the upper compensated transform of a semiconvex function exists and coincides with the center of the minimal bounding sphere of the corresponding Fréchet subdifferential. Several intermediate results of interest on their own are provided as well.
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compensated convex transforms
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convex function
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semiconvex function
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semiconcave function
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linear modulus
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general modulus
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singularity extraction
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minimal bounding sphere
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Fréchet subdifferential
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