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On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane

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Abstract

By using techniques of real analysis and weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the extended Hurwitz zeta function is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and some corollaries.

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Acknowledgements

M.Th. Rassias: I would like to express my gratitude to the J.S. Latsis Foundation for their financial support provided under the auspices of my current “Latsis Foundation Senior Fellowship” position.

B. Yang: This work is supported by the National Natural Science Foundation (Nos. 61370186 and 61640222), and Appropriative Researching Fund for Professors and Doctors, Guangdong University of Education (No. 2015ARF25). I am grateful for this help.

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Authors and Affiliations

  1. Institute of Mathematics, University of Zurich, 8057, Zurich, Switzerland

    Michael Th. Rassias

  2. Institute for Advanced Study Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ, 08540, USA

    Michael Th. Rassias

  3. Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700, Dolgoprudny, Russia

    Michael Th. Rassias

  4. Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510303, P.R. China

    Bicheng Yang

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  1. Michael Th. Rassias
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  2. Bicheng Yang
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Correspondence to Michael Th. Rassias.

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Rassias, M.T., Yang, B. On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane. Acta Appl Math 160, 67–80 (2019). https://doi.org/10.1007/s10440-018-0195-9

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  • DOI: https://doi.org/10.1007/s10440-018-0195-9

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