A kind of sharp Wirtinger inequalities

被引：0

作者：

Xu, Guiqiao ^{[1
]}

Liu, Yongping ^{[2
]}

Guo, Dandan ^{[2
]}

机构：

[1] Tianjin Normal Univ, Sch Math Sci, 393 Extens Bin Shui West Rd, Tianjin 300387, Peoples R China

[2] Beijing Normal Univ, Dept Math, 19 Xinjiekouwai St, Beijing 100875, Peoples R China

来源：

INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2024年 / 22卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Birkhoff interpolation; Lp-norm; eigenvalue; Wirtinger inequality; Picone inequality;

D O I：

10.1142/S0219691323500364

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

where f E W-q(n) [a, b] with at least n zeros (counting multiplicity) in [a, b]. First, based on the Hermite (Lagrange) interpolation, we express f as a Lagrange type (integral type) remainder. Second, we refer the computation of B-n,B-k,B-p,B-8 to the maximum value problem of a multivariate function, and we give the values of B(n,k,p,8)by finding the solution of the multivariate function aforementioned. At last, we refer the computation of Bn,k,p,q(1 = q < 8) to the norm of an integral operator. Our results are corrections and extensions to the results that appear in [J. C. Kuang, Applied Inequalities (Shandong Science and Technology Press, Jinan, 2004); A. Yu. Levin, Some estimates for a diff erentiable function, Dokl. Akad. Nauk SSSR 138 (1961) 37-38 (in Russian)].

引用

页数：17

共 50 条

[41] H∞ stabilisation of uncertain discrete time-delayed system with actuator saturation by using Wirtinger inequality [J].

Agrawal, Komal ;

Negi, Richa ;

Pal, Vipin Chandra ;

Patel, Vishwajeet .

INTERNATIONAL JOURNAL OF AUTOMATION AND CONTROL, 2023, 17 (01) :43-72

[42] Wirtinger inequality-based control design for an interconnected large-scale system with sampled controls [J].

Rehak, Branislav .

PROCEEDINGS OF THE 38TH CHINESE CONTROL CONFERENCE (CCC), 2019, :1009-1014

[43] Stability of aperiodic sampled-data systems — An augmented looped Lyapunov functional with wirtinger inequality approach [J].

Min Zheng ;

Hainan Yang ;

Yang Song ;

Jing Deng ;

Minrui Fei .

International Journal of Control, Automation and Systems, 2015, 13 :773-777

[44] Non-Fragile Sampled Control Design for an Interconnected Large-Scale System via Wirtinger Inequality [J].

Lynnyk, Volodymyr ;

Rehak, Branislav .

AXIOMS, 2024, 13 (10)

[45] H∞ analysis and switching control for uncertain discrete switched time-delay systems by discrete Wirtinger inequality [J].

Yu, Ker-Wei ;

Lien, Chang-Hua ;

Chang, Hao-Chin .

ADVANCES IN DIFFERENCE EQUATIONS, 2017,

[46] Anti-periodic solutions problem for inertial competitive neutral-type neural networks via Wirtinger inequality [J].

Bo Du .

Journal of Inequalities and Applications, 2019

[47] Sharp Estimates for Eigenfunctions of a Neumann Problem [J].

Brandolini, B. ;

Chiacchio, F. ;

Trombetti, C. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (11) :1317-1337

[48] Spectral asymptotics for δ-interactions on sharp cones [J].

Ourmieres-Bonafos, Thomas ;

Pankrashkin, Konstantin ;

Pizzichillo, Fabio .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (01) :566-589

[49] On Friedrichs inequalities for a disk [J].

Gadyl'shin, R. R. ;

Shishkina, E. A. .

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 281 :S44-S58

[50] THE PROPERTIES OF A KIND OF RANDOM SYMPLECTIC MATRICES [J].

闫庆友 .

Applied Mathematics and Mechanics(English Edition), 2002, (05) :590-596

← 1 2 3 4 5 →