A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function. Issue 9 (4th July 2018)

• Record Type: Journal Article
• Authors: Rassias, Michael Th.; Yang, Bicheng
• Is Part Of: Applicable analysis. Volume 97:Issue 9(2018)
• Page Start: 1505
• Page End: 1525
• Publication Date: 2018-07-04
• Subjects: Half-discrete Hilbert-type inequality -- Hermite–Hadamard's inequality -- weight function -- equivalent form -- Riemann zeta function; 26D15 -- 31A10 -- 31B10 -- 45P05 -- 47G10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1313411
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: By the use of Hermite–Hadamard's inequality and weight functions, a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic cotangent function and multi-parameters is given. The constant factor related to the Riemann zeta function is proved to be the best possible. The equivalent forms, two kinds of particular inequalities, the operator expressions and some equivalent reverses are considered.