# Some reverse Hölder inequalities with Specht's ratio on time scales

Volume 11, Issue 4, pp 444--455 Publication Date: March 10, 2018       Article History
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### Authors

A. A. El-Deeb - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. H. A. Elsennary - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. - Department of Mathematics, Faculty of Engineering, Sinai University, El Arish (45615), North Sinai, Egypt. Wing-Sum Cheung - Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.

### Abstract

In this article, we investigate some new reverse Hölder-type inequalities on an arbitrary time scale via the diamond-$\alpha$ dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues.

### Keywords

• Dynamic inequalities of Hölder type
• analysis techniques
• time scales
• Specht's ratio

•  26D10
•  26D15
•  26D20
•  34A12
•  34A40

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