TWO KINDS OF THE REVERSE HARDY-TYPE INTEGRAL INEQUALITIES WITH THE EQUIVALENT FORMS RELATED TO THE EXTENDED RIEMANN ZETA FUNCTION

被引：29

作者：

Rassias, Michael Th ^{[1
,2
,3
]}

Yang, Bicheng ^{[4
]}

Raigorodskii, Andrei ^{[2
,5
,6
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[2] Moscow Inst Phys & Technol, Inst Skiy D 9, Dolgoprudnyi 141700, Russia

[3] Inst Adv Study, Program Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540 USA

[4] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

[5] Moscow MV Lomonosov State Univ, Moscow 119991, Russia

[6] Buryat State Univ, Ulan Ude, Russia

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2018年 / 12卷 / 02期

关键词：

Hardy-type integral inequality; best possible constants; equivalent form; Riemann zeta function;

D O I：

10.2298/AADM180130011R

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Applying techniques of real analysis and weight functions, we study some equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a particular nonhomogeneous kernel. The constant factors are related to the Riemann zeta function and are proved to be best possible. In the form of applications, we deduce a few equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a particular homogeneous kernel. We also consider some corollaries as particular cases.

引用

页码：273 / 296

页数：24

共 24 条

[1]

[Anonymous], 2004, Applied inequalities

[2]

Arpad B., 2006, J INEQUALITIES APPL, V2006, P28582

[3]

Hardy G., 1967, Inequalities

[4]

HARDY GH, 1925, P LONDON MATH SOC, V23

[5]

Hong Y., 2005, INEQ PURE APPL MATH, V6, P92

[6]

[洪勇 Hong Yong], 2017, [吉林大学学报. 理学版, Journal of Jilin University. Science Edition], V55, P189

[7]

Krnic M, 2005, PUBL MATH-DEBRECEN, V67, P315

[8]

KUANG J. C., 2015, Real and functional analysis (Continuation)

[9] On inequalities of Hilbert's type [J].

Li, Yongjin ;

He, Bing .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 76 (01) :1-13

[10]

Mitrinovic D. S., 1991, INEQUALITIES FUNCTIO

← 1 2 3 →