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

Volume 11, Issue 4, pp 444--455 http://dx.doi.org/10.22436/jnsa.011.04.01 Publication Date: March 10, 2018       Article History

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.


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