A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function

Rassias, Michael Th.; Yang, Bicheng

doi:10.22075/ijnaa.2016.375

A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function

Document Type : Research Paper

Authors

Michael Th. Rassias ¹

Bicheng Yang ²

¹ Institute of Mathematics, University of Zurich, CH-8057, Zurich, Switzerland \ & Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA

² Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China

10.22075/ijnaa.2016.375

Abstract

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the reverses and some particular cases are also considered.

Keywords

Hardy-Hilbert-type inequality

extended Riemann-zeta function

Hurwitz zeta function

Gamma function

weight function

equivalent form

operator