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

Authors

  • Bicheng Yang Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
  • Michael Th. Rassias 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
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.

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Journal title

volume 7  issue 2

pages  1- 27

publication date 2016-06-01

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