On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Hyperbolic Tangent Function and Parameters

Michael Th. Rassias (), Bicheng Yang () and Andrei Raigorodskii ()
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Michael Th. Rassias: University of Zurich, Institute of Mathematics
Bicheng Yang: Guangdong University of Education, Department of Mathematics
Andrei Raigorodskii: Moscow Institute of Physics and Technology

A chapter in Approximation Theory and Analytic Inequalities, 2021, pp 405-434 from Springer

Abstract: Abstract In this paper, introducing multi-parameters and using properties of series, we prove a half-discrete Hilbert-type inequality in the whole plane with kernel in terms of the hyperbolic tangent function. The constant factor related to the Riemann zeta function and the gamma function is proved to be the best possible. In the form of applications, we also present equivalent forms, a few particular inequalities, operator expressions and reverses.

Keywords: Half-discrete Hilbert-type inequality; Weight function; Equivalent form; Operator expression; Riemann zeta function; Reverse; 26D15; 31A10; 47A05 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-60622-0_22

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DOI: 10.1007/978-3-030-60622-0_22

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