An existence criterion for a smooth function under constraints
type: Item
instance of: scholarly article
title: An existence criterion for a smooth function under constraints
zbMATH Open document ID: 1156.26002
DOI: 10.1134/S0001434607090027
author: A. A. Vasil'eva
published in: Mathematical Notes
publication date: 2008-09-03T00:00:00Z
review text: 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.
reviewed by: Vladimír Janiš
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 5319840
zbMATH Keywords: smooth function
zbMATH Keywords: locally Lipschitz function
zbMATH Keywords: bounded derivative
MaRDI profile type: Publication
cites work: On nonlinear projections in Banach spaces
cites work: On Lipschitz selections of affine-set valued mappings
cites work: The embedding of proximinal sets
cites work: Q5575875
cites work: Approximation properties of certain sets in the space of continuous functions
cites work: Q5565773
full work available at URL: s0001434607090027
OpenAlex ID: W2318196904
Recommended article: Q3737870
Recommended article: Q3688991
Recommended article: Sufficient conditions for the Hölder smoothness of a function
Recommended article: Q3331806
Recommended article: Convexity Conditions and Intersections with Smooth Functions
Recommended article: Q4714923
Recommended article: Extremum conditions for smooth problems with equality-type constraints
Recommended article: On existence and uniqueness verification for non-smooth functions
Recommended article: An extremum principle for smooth problems
Recommended article: Q4203142
description: scientific article; zbMATH DE number 5319840