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


علمی-پژوهشی (وزارت علوم)/ISC (27 صفحه - از 1 تا 27)


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.

کلیدواژه ها:

Operator ،Hardy-Hilbert-type inequality ،extended Riemann-zeta function ،Hurwitz zeta function ،Gamma function ،weight function ،equivalent form

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