Title of article :
A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
Author/Authors :
Rassias, Michael Th University of Zurich - Zurich - Switzerland & Institute for Advanced Study - Program in Interdisciplinary Studies - Princeton, USA , Yang, Bicheng Department of Mathematics - Guangdong University of Education - Guangzhou, P. R. China
Abstract :
By the method of weight coeffcients, 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
Journal title :
Astroparticle Physics
