Young's integral inequality with upper and lower bounds

Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding r...

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Bibliographic Details
Main Authors:	Douglas R. Anderson, Steven Noren, Brent Perreault
Format:	Article
Language:	English
Published:	Texas State University 2011-06-01
Series:	Electronic Journal of Differential Equations
Subjects:	Young's inequality monotone functions Pochhammer lower factorial difference equations time scales
Online Access:	http://ejde.math.txstate.edu/Volumes/2011/74/abstr.html

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spelling	doaj-08df2363c5184784baa0e32a23cf4d1f2020-11-24T20:55:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-06-01201174,110Young's integral inequality with upper and lower boundsDouglas R. AndersonSteven NorenBrent PerreaultYoung's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding results for difference equations are given, and several examples are included. We extend these results to piecewise-monotone functions as well. http://ejde.math.txstate.edu/Volumes/2011/74/abstr.htmlYoung's inequalitymonotone functionsPochhammer lower factorialdifference equationstime scales
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Douglas R. Anderson Steven Noren Brent Perreault
spellingShingle	Douglas R. Anderson Steven Noren Brent Perreault Young's integral inequality with upper and lower bounds Electronic Journal of Differential Equations Young's inequality monotone functions Pochhammer lower factorial difference equations time scales
author_facet	Douglas R. Anderson Steven Noren Brent Perreault
author_sort	Douglas R. Anderson
title	Young's integral inequality with upper and lower bounds
title_short	Young's integral inequality with upper and lower bounds
title_full	Young's integral inequality with upper and lower bounds
title_fullStr	Young's integral inequality with upper and lower bounds
title_full_unstemmed	Young's integral inequality with upper and lower bounds
title_sort	young's integral inequality with upper and lower bounds
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2011-06-01
description	Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding results for difference equations are given, and several examples are included. We extend these results to piecewise-monotone functions as well.
topic	Young's inequality monotone functions Pochhammer lower factorial difference equations time scales
url	http://ejde.math.txstate.edu/Volumes/2011/74/abstr.html
work_keys_str_mv	AT douglasranderson youngsintegralinequalitywithupperandlowerbounds AT stevennoren youngsintegralinequalitywithupperandlowerbounds AT brentperreault youngsintegralinequalitywithupperandlowerbounds
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Young's integral inequality with upper and lower bounds

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