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An Extension of Hardy–Hilbert’s Inequality

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

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Abstract

By using the way of weight coefficient and the improved Euler-Maclaurin’s summation formula, a new extension of Hardy–Hilbert’s inequality with multi-parameter and a best constant factor is obtained, and the equivalent form is considered.

Mathematics Subject Classification (2000): Primary 26D15

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Acknowledgements

This work is supported by the Emphases Natural Science Foundation of Guangdong Institution, Higher Learning, College and University (No. 05Z026), and Guangdong Natural Science Foundation (No. 7004344).

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Authors and Affiliations

  1. Department of Mathematics, Guangdong Education Institute, Guangzhou, 510303, China

    Bicheng Yang

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  1. Bicheng Yang
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Correspondence to Bicheng Yang .

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Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Yang, B. (2011). An Extension of Hardy–Hilbert’s Inequality. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_46

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