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

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Rassias Michael Th.; Yang Bicheng

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Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2016 | Volume:7 | Issue:2 Page(s): 1-27

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Title

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

Author(s)

Rassias Michael Th. | Yang Bicheng

Keywords

Hardy-Hilbert-type inequality

extended Riemann-zeta function

Hurwitz zeta function

Gamma function

weight function

equivalent form

operator

Abstract

By the method of weight coe cients, 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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APA: Copy

Rassias, Michael Th., & Yang, Bicheng. (2016). A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 7(2), 1-27. SID. https://sid.ir/paper/340723/en

Vancouver: Copy

Rassias Michael Th., Yang Bicheng. A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2016;7(2):1-27. Available from: https://sid.ir/paper/340723/en

IEEE: Copy

Michael Th. Rassias, and Bicheng Yang, “A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 7, no. 2, pp. 1–27, 2016, [Online]. Available: https://sid.ir/paper/340723/en

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