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Equivalent Properties of Parameterized Hilbert-Type Integral Inequalities

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Mathematical Analysis and Applications

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

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Abstract

By the use of the techniques of real analysis and the weight functions, a few equivalent statements of a general Hilbert-type integral inequality with the nonhomogeneous kernel related to another inequality, the parameters and the integral of kernel are obtained. The best possible constant factor is given. As a corollary, a few equivalent statements of a general Hilbert-type integral inequality with the homogeneous kernel and a best possible constant factor are deduced. Moreover, we also study the case of the reverses. The operator expressions, a few particular cases and some examples are considered.

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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). I’m grateful for this help.

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Authors and Affiliations

  1. Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, People’s Republic of 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, 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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Yang, B. (2019). Equivalent Properties of Parameterized Hilbert-Type Integral Inequalities. 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_23

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