An existence criterion for a smooth function under constraints (Q942048)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An existence criterion for a smooth function under constraints |
scientific article; zbMATH DE number 5319840
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence criterion for a smooth function under constraints |
scientific article; zbMATH DE number 5319840 |
Statements
An existence criterion for a smooth function under constraints (English)
0 references
3 September 2008
0 references
A problem of existence of a real function \(f\) such that \(f_1 \leq f \leq f_2\) for given \(f_1, f_2\) fulfilling some requirements on its derivative is studied. These requirements are: being locally Lipschitz with bounded gradient in the first part of the paper and having the first derivative bounded between two prescribed continuous functions in its second part. In both cases necessary and sufficient conditions for existence are found.
0 references
smooth function
0 references
locally Lipschitz function
0 references
bounded derivative
0 references
0.8675846
0 references
0.86407435
0 references
0 references
0.85770357
0 references
0.8573494
0 references
