On Opial-Traple type inequalities for β-partial derivatives

In the paper, we introduce a new partial derivative call it β-partial derivatives as the most natural extensions of the limit definitions of the partial derivative and the β-derivative, which obeys classical properties including: continu...

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Main Authors:	Chang-Jian Zhao, Wing-Sum Cheung
Format:	Article
Language:	English
Published:	AIMS Press 2020-07-01
Series:	AIMS Mathematics
Subjects:	<i>β</i>-derivative partial derivative <i>β</i>-partial derivative cauchy-schwarz inequality
Online Access:	https://www.aimspress.com/article/10.3934/math.2020366/fulltext.html

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spelling	doaj-9d87f0774895471dab4cd626c8f124272020-11-25T03:06:00ZengAIMS PressAIMS Mathematics2473-69882020-07-01565716572310.3934/math.2020366On Opial-Traple type inequalities for <em>β</em>-partial derivativesChang-Jian Zhao0Wing-Sum Cheung11 Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China2 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong KongIn the paper, we introduce a new partial derivative call it <em>β</em>-<em>partial derivatives</em> as the most natural extensions of the limit definitions of the partial derivative and the <em>β</em>-derivative, which obeys classical properties including: continuity, linearity, product rule, quotient rule, power rule, chain rule and vanishing derivatives for constant functions. As applications, we establish some new Opial-Traple type inequalities for the <em>β</em>-partial derivatives.https://www.aimspress.com/article/10.3934/math.2020366/fulltext.html<i>β</i>-derivativepartial derivative<i>β</i>-partial derivativecauchy-schwarz inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Chang-Jian Zhao Wing-Sum Cheung
spellingShingle	Chang-Jian Zhao Wing-Sum Cheung On Opial-Traple type inequalities for <em>β</em>-partial derivatives AIMS Mathematics <i>β</i>-derivative partial derivative <i>β</i>-partial derivative cauchy-schwarz inequality
author_facet	Chang-Jian Zhao Wing-Sum Cheung
author_sort	Chang-Jian Zhao
title	On Opial-Traple type inequalities for <em>β</em>-partial derivatives
title_short	On Opial-Traple type inequalities for <em>β</em>-partial derivatives
title_full	On Opial-Traple type inequalities for <em>β</em>-partial derivatives
title_fullStr	On Opial-Traple type inequalities for <em>β</em>-partial derivatives
title_full_unstemmed	On Opial-Traple type inequalities for <em>β</em>-partial derivatives
title_sort	on opial-traple type inequalities for <em>β</em>-partial derivatives
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2020-07-01
description	In the paper, we introduce a new partial derivative call it <em>β</em>-<em>partial derivatives</em> as the most natural extensions of the limit definitions of the partial derivative and the <em>β</em>-derivative, which obeys classical properties including: continuity, linearity, product rule, quotient rule, power rule, chain rule and vanishing derivatives for constant functions. As applications, we establish some new Opial-Traple type inequalities for the <em>β</em>-partial derivatives.
topic	<i>β</i>-derivative partial derivative <i>β</i>-partial derivative cauchy-schwarz inequality
url	https://www.aimspress.com/article/10.3934/math.2020366/fulltext.html
work_keys_str_mv	AT changjianzhao onopialtrapletypeinequalitiesforembempartialderivatives AT wingsumcheung onopialtrapletypeinequalitiesforembempartialderivatives
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On Opial-Traple type inequalities for <em>β</em>-partial derivatives

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