A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function. (English) Zbl 1393.26028
Summary: By the use of Hermite-Hadamard’s inequality and weight functions, a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic cotangent function and multi-parameters is given. The constant factor related to the Riemann zeta function is proved to be the best possible. The equivalent forms, two kinds of particular inequalities, the operator expressions and some equivalent reverses are considered.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
Keywords:
half-discrete Hilbert-type inequality; Hermite-Hadamard inequality; weight function; equivalent form; Riemann zeta functionReferences:
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