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Mathematical Analysis and Applications pp 511–528Cite as

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

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 154))

Abstract

By the use of the methods of real analysis and the weight functions, a few equivalent conditions of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The best possible constant factor is related to the extended Riemann zeta function. As applications, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and a few particular cases.

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Acknowledgements

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

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Authors and Affiliations

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

    Michael Th. Rassias

  2. Institute for Advanced Study Program in Interdisciplinary Studies, Princeton, NJ, USA

    Michael Th. Rassias

  3. Department of Mathematics, Guangdong University of Education, Guangdong, People’s Republic of China

    Bicheng Yang

Authors
  1. Michael Th. Rassias
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  2. Bicheng Yang
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Corresponding author

Correspondence to Bicheng Yang .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Rassias, M.T., Yang, B. (2019). On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_19

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