A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function |
| |
| Authors: | Michael Th. Rassias Bicheng Yang |
| |
| Affiliation: | 1. Institute of Mathematics, University of Zurich , Zurich, Switzerland.;2. Institute for Advanced Study, Program in Interdisciplinary Studies , Princeton, NJ, USA.;3. Department of Mathematics, Guangdong University of Education , Guangzhou, P.R. China. |
| |
| 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. |
| |
| Keywords: | Half-discrete Hilbert-type inequality Hermite–Hadamard’s inequality weight function equivalent form Riemann zeta function |
|
|
