一个较为精密的Hardy-Hilbert型不等式的加强及应用
|
摘要
对Hardy-Hilbert不等式进行了研究,并将其进一步改进如下:若p>1,1/p+1/q=1,α≥e~(7/6),r,s∈R,a_n,b_n≥0,使得0 After studying on Hardy-Hilbert's inequality,the improvements as following are achieved:if p>1,1/p+1/q=1,α≥e~(7/6),r,s∈R,a_n,b_n≥0,and 0
引文
[1]HARDY G H,LITTLEWOOD J E,PóLYA G.Inequalities[M].lin-coln:Cambridge Univ Press,1952.
[2]YANG B C.On a strengthened version of the more accurate HardyHilberts inequality[J].Acta Math Sinica(N.S.),1999,42(6):1103-1110.
[3]隆建军.一个推广的Hardy-Hilbert不等式及应用[J].佳木斯大学学报(自然科学版),2013,3(31):456-460.
[4]PACHPATTE B G.On some new inequalities similar to Hilbert'sinequality[J].J Math Anal Appl,1998,226(1):166-179.
[5]罗静,隆建军.关于一个Hardy-Hilbert型不等式的改进与推广[J].四川理工学院学报(自然科学版),2013,26(5):67-70.
[6]王卫宏,方波漪.一个Hilbert型不等式的推广与加强[J].五邑大学学报(自然科学版),2006,20(4):19-23.
[7]隆建军.一个Hardy-Hilbert型不等式的推广与加强[J].山东理工大学学报(自然科学版),2012,26(2):25-28.
[8]KUANG J C,DEBNATH L.On new generalizations of Hilberts in-equality and their applications[J].J Math Anal Appl,2000,245(1):248-265.
[2]YANG B C.On a strengthened version of the more accurate HardyHilberts inequality[J].Acta Math Sinica(N.S.),1999,42(6):1103-1110.
[3]隆建军.一个推广的Hardy-Hilbert不等式及应用[J].佳木斯大学学报(自然科学版),2013,3(31):456-460.
[4]PACHPATTE B G.On some new inequalities similar to Hilbert'sinequality[J].J Math Anal Appl,1998,226(1):166-179.
[5]罗静,隆建军.关于一个Hardy-Hilbert型不等式的改进与推广[J].四川理工学院学报(自然科学版),2013,26(5):67-70.
[6]王卫宏,方波漪.一个Hilbert型不等式的推广与加强[J].五邑大学学报(自然科学版),2006,20(4):19-23.
[7]隆建军.一个Hardy-Hilbert型不等式的推广与加强[J].山东理工大学学报(自然科学版),2012,26(2):25-28.
[8]KUANG J C,DEBNATH L.On new generalizations of Hilberts in-equality and their applications[J].J Math Anal Appl,2000,245(1):248-265.