Abstract
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.
Acknowledgements
We are grateful for their help. The authors would like to express their thanks to Ts. Batbold, M. Krnic and J. C. Kuang for reading a preliminary version of the paper and for providing useful comments.
Disclosure statement
No potential conflict of interest was reported by the authors.