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On a Relation Between the Hardy–Hilbert and Gabriel Inequalities

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Handbook of Functional Equations

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 95))

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Abstract

In this chapter, we establish some new generalizations of Azar’s results, which are relations between the Hardy–Hilbert inequality and the Gabriel inequality. As an application, we obtain a sharper form of the general Hardy-Hilbert inequality. The integral analogues of our main results are also given. Some Gabriel-type inequalities are also considered.

Mathematics Subject Classification (2000): Primary 26D15, Secondary 05E05

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Acknowledgements

We would like to express our gratitude to Prof. Mario Krnić for reading the manuscript and for his very helpful remarks.

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Correspondence to Tserendorj Batbold .

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Adiyasuren, V., Batbold, T. (2014). On a Relation Between the Hardy–Hilbert and Gabriel Inequalities. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_1

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