A More Accurate Half-Discrete Hardy-Hilbert-Type Inequality with the Best Possible Constant Factor Related to the Extended Riemann-Zeta Function

2015/12/13 by Michael Th. Rassias, Rassias, Michael Th., Bicheng Yang +1 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.1512.04063

arxiv created 2015/12/13 · openalex publication_date 2015/12/13 · arxiv updated 2015/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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• A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function

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