Hardy-Leindler Type Inequalities on Time Scales

被引：15
作者：
Saker, S. H. [1 ]
机构：
[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt
来源：
APPLIED MATHEMATICS & INFORMATION SCIENCES | 2014年 / 8卷 / 06期
关键词：
Hardy's inequality; Leindler's inequality; time scales;
D O I：
10.12785/amis/080635
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities, as special cases, when T = R contain some integral inequalities and when T = N contain the discrete inequalities due to Leindler. The main results will be proved by using the Holder inequality and a simple consequence of Keller's chain rule on time scales. From our results, as applications, we will derive some new continuous and discrete Wirtinger type inequalities. The technique in this paper is completely different from the technique used by Leindler to prove his main results.
引用
收藏
页码：2975 / 2981
页数：7
相关论文
共 30 条
[1]   SOME DYNAMIC WIRTINGER-TYPE INEQUALITIES AND THEIR APPLICATIONS [J].
Agarwal, Ravi P. ;
Bohner, Martin ;
O'Regan, Donal ;
Saker, Samir H. .
PACIFIC JOURNAL OF MATHEMATICS, 2011, 252 (01) :1-18
[2]  
Beesack P.R., 1961, Pac. J. Math., V11, P39, DOI DOI 10.2140/PJM.1961.11.39
[3]  
Bohner M., 2001, Dynamic Equations on Time Scales: An Introduction with Applications, DOI DOI 10.1007/978-1-4612-0201-1
[4]  
Bohner M., 2003, Advances in Dynamic Equations on Time Scales, DOI DOI 10.1007/978-0-8176-8230-9
[5]  
ELLIOTT EDWIN BAILEY, 1926, J. London Math. Soc., V1, P93
[6]   Note on a theorem of Hilbert. [J].
Hardy, GH .
MATHEMATISCHE ZEITSCHRIFT, 1920, 6 :314-317
[7]  
Hardy GH., 1928, Messenger Math, V57, P12
[8]  
Hardy GH., 1925, Messenger Math, V54, P150
[9]  
Hardy Godfrey Harold, 1952, Inequalities, V2nd
[10]  
Hilger S., 1990, Result math, V18, P18, DOI [DOI 10.1007/BF03323153, 10.1007/BF03323153]
123