On Opial-Wirtinger type inequalities

Chang-jian Zhao; Chang-jian Zhao

doi:10.3934/math.2020087

AIMS Mathematics

2020, Volume 5, Issue 2: 1275-1283. doi: 10.3934/math.2020087

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Research article

On Opial-Wirtinger type inequalities

Chang-jian Zhao ^,

Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China

Received: 24 October 2019 Accepted: 07 January 2020 Published: 19 January 2020
MSC : 26D15

In the present paper we establish some new Opial-Wirtinger's type inequalities involving Katugampola partial derivatives. These new results in special cases yield Agarwal and Pang's, Traple's and Pachpatte's inequalities and provide new estimates on inequality of this type.
- Katugampola partial derivatives,
- Young’s inequality,
- Opial’s inequality,
- Wirtinger’s inequality,
- Hölder’s inequality
Citation: Chang-jian Zhao. On Opial-Wirtinger type inequalities[J]. AIMS Mathematics, 2020, 5(2): 1275-1283. doi: 10.3934/math.2020087

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Abstract

In the present paper we establish some new Opial-Wirtinger's type inequalities involving Katugampola partial derivatives. These new results in special cases yield Agarwal and Pang's, Traple's and Pachpatte's inequalities and provide new estimates on inequality of this type.

References

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