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Half-Discrete Hilbert-Type Inequalities, Operators and Compositions

In: Handbook of Functional Equations

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  • Bicheng Yang

    (Guangdong University of Education)

Abstract

In this chapter, using the methods of weight functions and technique of real analysis, a half-discrete Hilbert-type inequality with a homogeneous kernel and a best possible constant factor is provided. Some equivalent representations, two types of reverses, the operator expressions as well as some particular examples are obtained. Furthermore, we also consider some strengthened versions of half-discrete Hilbert’s inequality relating to Euler constant, the related inequalities and operators with the non-homogeneous kernel, and two kinds of compositions of two operators in certain conditions.

Suggested Citation

  • Bicheng Yang, 2014. "Half-Discrete Hilbert-Type Inequalities, Operators and Compositions," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 459-534, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1246-9_19
    DOI: 10.1007/978-1-4939-1246-9_19
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