International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 403-408
doi:10.1155/S0161171298000556
On new strengthened Hardy-Hilbert's inequality
Bicheng Yang1
and Lokenath Debnath2
1Department of Mathematics, Guangdong Education College, Guangdong, Guangzhou 510303, China
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Abstract
In this paper, a new inequality for the weight coefficient ω(q,n) in the form ω(q,n):=∑m=1∞1m+n(nm)1/q <πsin(π/p)−12π1/p+n−1/q(q>1,1p+1q=1,n∈N) is proved. This is followed by a strengthened version ofthe Hardy-Hilbert inequality.