On Hilbert’s Inequality for Double Series and Its Applications
نویسنده
چکیده
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.
منابع مشابه
On 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 کاملOn a New Strengthened Version of a Hardy-hilbert Type Inequality and Applications
By improving an inequality of the weight coefficient, we give a new strengthened version of Hardy-Hilbert’s type inequality. As its applications, we build some strengthened versions of the equivalent form and some particular results.
متن کاملOn a strengthened Hardy-Hilbert’s type inequality
In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.
متن کاملAn Improvement of Some Inequalities Similar to Hilbert’s Inequality
We give an improvement of some inequalities similar to Hilbert’s inequality involving series of nonnegative terms. The integral analogies of the main results are also given. 2000 Mathematics Subject Classification. 26D15.
متن کاملOn Hilbert's Inequality for Double Series and Its Applications
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.
متن کامل