New multiplicative higher order dynamic inequalities of opial type

Safi S. Rabie; S. H. Saker; D. O'regan; R. P. Agarwal

doi:10.7153/mia-19-03

New multiplicative higher order dynamic inequalities of opial type

Safi S. Rabie
, S. H. Saker
, D. O'regan
, R. P. Agarwal

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

In this paper, we prove some new multiplicative dynamic inequalities of Opial type on a time scale T. The main results will be proved by using Hölder's inequality, the chain rule and some basic dynamic inequalities designed and proved for this purpose. As special cases, we will derive some continuous and discrete inequalities from the main results.

Original language	English
Pages (from-to)	33-49
Number of pages	17
Journal	Mathematical Inequalities and Applications
Volume	19
Issue number	1
DOIs	https://doi.org/10.7153/mia-19-03
Publication status	Published - Jan 2016

Keywords

Opial's inequality
Partial derivatives
Shum's inequalities
Time scales

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title = "New multiplicative higher order dynamic inequalities of opial type",

abstract = "In this paper, we prove some new multiplicative dynamic inequalities of Opial type on a time scale T. The main results will be proved by using H{\"o}lder's inequality, the chain rule and some basic dynamic inequalities designed and proved for this purpose. As special cases, we will derive some continuous and discrete inequalities from the main results.",

keywords = "Opial's inequality, Partial derivatives, Shum's inequalities, Time scales",

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year = "2016",

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AU - Rabie, Safi S.

AU - Saker, S. H.

AU - O'regan, D.

AU - Agarwal, R. P.

PY - 2016/1

Y1 - 2016/1

N2 - In this paper, we prove some new multiplicative dynamic inequalities of Opial type on a time scale T. The main results will be proved by using Hölder's inequality, the chain rule and some basic dynamic inequalities designed and proved for this purpose. As special cases, we will derive some continuous and discrete inequalities from the main results.

AB - In this paper, we prove some new multiplicative dynamic inequalities of Opial type on a time scale T. The main results will be proved by using Hölder's inequality, the chain rule and some basic dynamic inequalities designed and proved for this purpose. As special cases, we will derive some continuous and discrete inequalities from the main results.

KW - Opial's inequality

KW - Partial derivatives

KW - Shum's inequalities

KW - Time scales

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U2 - 10.7153/mia-19-03

DO - 10.7153/mia-19-03

M3 - Article

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VL - 19

SP - 33

EP - 49

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

New multiplicative higher order dynamic inequalities of opial type

Abstract

Keywords

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