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

Author(s):

Michael Th. Rassias * , Bicheng Yang

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

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:7 Issue: 2, Winter - Spring 2016
Pages:
1 to 27
https://www.magiran.com/p1641823