An Extension of the Hilbert’s Integral Inequality
نویسندگان
چکیده
where the constant factor π 1 is the best possible. This is the famous Hilbert’s integral inequality see 1, 2 . Owing to the importance of the Hilbert’s inequality and the Hilberttype inequality in analysis and applications, some mathematicians have been studying them. Recently, various improvements and extensions of 1.1 appear in a great deal of papers see 3–11 , etc. . Specially, Gao and Hsu enumerated the research articles more than 40 in the paper 6 . The purpose of the present paper is to establish the Hilbert-type inequality of the form
منابع مشابه
On a New Multiple Extension of Hilbert’s Integral Inequality
This paper gives a new multiple extension of Hilbert’s integral inequality with a best constant factor, by introducing a parameter λ and the Γ function. Some particular results are obtained.
متن کاملSome Extensions of Hilbert’s Integral Inequality
In this paper we introduce a new extension of Hilbert's integral inequality with a best constant factor involving the hypergeometric function. The equivalent form and some examples will be given.
متن کاملA Further Generalization of Hardy-hilbert’s Integral Inequality with Parameter and Applications
In this paper, by introducing some parameters and by employing a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder’s theorem is given.
متن کاملOn Some Extensions of Hardy-Hilbert’s Inequality and Applications
Laith Emil Azar Department of Mathematics, Al Al-Bayt University, P.O. Box. 130095, Mafraq 25113, Jordan Correspondence should be addressed to Laith Emil Azar, azar [email protected] Received 23 October 2007; Accepted 2 January 2008 Recommended by Shusen Ding By introducing some parameters we establish an extension of Hardy-Hilbert’s integral inequality and the corresponding inequality for series...
متن کاملA Relation to Hardy-hilbert’s Integral Inequality and Mulholland’s Inequality
This paper deals with a relation between Hardy-Hilbert’s integral inequality and Mulholland’s integral inequality with a best constant factor, by using the Beta function and introducing a parameter λ. As applications, the reverse, the equivalent form and some particular results are considered.
متن کامل