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On a Hilbert-Type Integral Inequality in the Whole Plane

In: Applications of Nonlinear Analysis

Author

Listed:
  • Michael Th. Rassias

    (University of Zurich
    Moscow Institute of Physics and Technology
    Institute for Advanced Study, Program in Interdisciplinary Studies)

  • Bicheng Yang

    (Guangdong University of Education)

Abstract

By using methods of real analysis and weight functions, we prove a new Hilbert-type integral inequality in the whole plane with non-homogeneous kernel and a best possible constant factor. As applications, we also consider the equivalent forms, some particular cases and the operator expressions.

Suggested Citation

  • Michael Th. Rassias & Bicheng Yang, 2018. "On a Hilbert-Type Integral Inequality in the Whole Plane," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 665-679, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-89815-5_23
    DOI: 10.1007/978-3-319-89815-5_23
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    Cited by:

    1. Jianquan Liao & Shanhe Wu & Bicheng Yang, 2020. "On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    2. Bicheng Yang & Shanhe Wu & Jianquan Liao, 2020. "On a New Extended Hardy–Hilbert’s Inequality with Parameters," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    3. Bicheng Yang & Shanhe Wu & Aizhen Wang, 2019. "On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters," Mathematics, MDPI, vol. 7(11), pages 1-12, November.

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