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

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

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

International Journal of Nonlinear Analysis and Applications
Volume 7, Issue 2 - Serial Number 2
Winter and Spring 2016
Pages 1-27

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