Global smoothness preservation and the variation-diminishing property
<p/> <p>In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators. Under certain additional assumptions it is shown that the variation-diminishing propert...
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Series: | Journal of Inequalities and Applications |
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doaj-097082c610534f66802f30804d9a11402020-11-25T00:29:56ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1999-01-0119992126510Global smoothness preservation and the variation-diminishing propertyGavrea IoanKacsó Daniela PZhou Ding-XuanGonska Heinz HCottin Claudia<p/> <p>In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators. Under certain additional assumptions it is shown that the variation-diminishing property is the stronger one. It is also demonstrated, however, that there are positive linear operators giving an optimal pointwise degree of approximation, and which preserve global smoothness, monotonicity and convexity, but are not variation-diminishing.</p>http://www.journalofinequalitiesandapplications.com/content/4/126510Global smoothness preservationVariation-diminishing propertyPositive linear operators |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Gavrea Ioan Kacsó Daniela P Zhou Ding-Xuan Gonska Heinz H Cottin Claudia |
spellingShingle |
Gavrea Ioan Kacsó Daniela P Zhou Ding-Xuan Gonska Heinz H Cottin Claudia Global smoothness preservation and the variation-diminishing property Journal of Inequalities and Applications Global smoothness preservation Variation-diminishing property Positive linear operators |
author_facet |
Gavrea Ioan Kacsó Daniela P Zhou Ding-Xuan Gonska Heinz H Cottin Claudia |
author_sort |
Gavrea Ioan |
title |
Global smoothness preservation and the variation-diminishing property |
title_short |
Global smoothness preservation and the variation-diminishing property |
title_full |
Global smoothness preservation and the variation-diminishing property |
title_fullStr |
Global smoothness preservation and the variation-diminishing property |
title_full_unstemmed |
Global smoothness preservation and the variation-diminishing property |
title_sort |
global smoothness preservation and the variation-diminishing property |
publisher |
SpringerOpen |
series |
Journal of Inequalities and Applications |
issn |
1025-5834 1029-242X |
publishDate |
1999-01-01 |
description |
<p/> <p>In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators. Under certain additional assumptions it is shown that the variation-diminishing property is the stronger one. It is also demonstrated, however, that there are positive linear operators giving an optimal pointwise degree of approximation, and which preserve global smoothness, monotonicity and convexity, but are not variation-diminishing.</p> |
topic |
Global smoothness preservation Variation-diminishing property Positive linear operators |
url |
http://www.journalofinequalitiesandapplications.com/content/4/126510 |
work_keys_str_mv |
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