An Extension of the Hilbert's Integral Inequality. (27th September 2009)

• Record Type: Journal Article
• Authors: Yu, Zhou; Xuemei, Gao; Mingzhe, Gao
• Other Names: Cheung Wing-Sum Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-09-27
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/158690
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parametersm ( m ∈ N ) andλ ( λ > 0 ) . The constant factors expressed by the Euler number andπ as well as by the Bernoulli number andπ, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.