A Reverse Hardy-Hilbert's Inequality Involving One Partial Sum as the Terms of Double Series. (21st April 2022)

• Record Type: Journal Article
• Authors: Yang, Bicheng; Wu, Shanhe; Huang, Xingshou
• Other Names: Drihem Douadi Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-04-21
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2175463
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, by constructing proper weight coefficients and utilizing the Euler-Maclaurin summation formula and the Abel partial summation formula, we establish reverse Hardy-Hilbert's inequality involving one partial sum as the terms of double series. On the basis of the obtained inequality, the equivalent conditions of the best possible constant factor associated with several parameters are discussed. Finally, we illustrate that more reverse inequalities of Hardy-Hilbert type can be generated from the special cases of the present results.