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Open AccessArticle

More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

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Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
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Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
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Department of Mathematics and Computer Science, Faculty of Science, Beni- Suef University, Beni-Suef, Egypt
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Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia
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Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1716; https://doi.org/10.3390/sym12101716
Received: 7 August 2020 / Revised: 23 September 2020 / Accepted: 24 September 2020 / Published: 18 October 2020
(This article belongs to the Special Issue Theory and Applications of Special Functions in Mathematical Physics)
In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R. View Full-Text
Keywords: Hölder’s inequality; generalization; refinement; diamond-α integral; time scale Hölder’s inequality; generalization; refinement; diamond-α integral; time scale
MDPI and ACS Style

Zakarya, M.; Abd El-Hamid, H.A.; AlNemer, G.; Rezk, H.M. More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral. Symmetry 2020, 12, 1716.

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