Inequalities on time scales: A survey

被引：265

作者：

Agarwal, R ^{[1
]}

Bohner, M

Peterson, A

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 119260, Singapore

[2] Univ Missouri, Dept Math & Stat, Rolla, MO 65409 USA

[3] Univ Nebraska, Dept Math & Stat, Lincoln, NE 68588 USA

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2001年 / 4卷 / 04期

关键词：

time scales; dynamic equations; measure chains;

D O I：

10.7153/mia-04-48

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The study of dynamic equations on time scales, which g-ocs back to its founder Stefan Hilger (1988), is an area of mathematics which is currently receiving considerable attention. Although the basic aim of this is to unify the study of differential and difference equations, it also extends these classical cases to cases "in between". In this paper we present time scales versions of the inequalities: Holder, Cauchy-Schwarz, Minkowski, Jensen, Gronwall, Bernoulli, Bihari, Opial, Wirtinger, and Lyapunov.

引用

页码：535 / 557

页数：23

共 16 条

[1]

AGARWAL R, 2000, UNPUB DYNAMIC EQUATI

[2]

Agarwal R. P., 1999, RESULTS MATH, V35, P3, DOI [DOI 10.1007/BF03322019, 10.1007/BF03322019]

[3] Quadratic functionals for second order matrix equations on time scales [J].

Agarwal, RP ;

Bohner, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 33 (07) :675-692

[4]

AGARWAL RP, 1995, OPIAL INEQUALITIES A

[5]

[Anonymous], 1999, Pure and Applied Mathematics (New York)

[6]

AULBACH B, 1990, MATH RES, V59, P9

[7] Asymptotic behavior of dynamic equations on time scales [J].

Bohner, M ;

Lutz, DA .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2001, 7 (01) :21-50

[8]

BOHNER M, 2000, IN PRESS J INEQUAL A

[9]

BOHNER M, 2000, IN PRESS J DIFFER EQ

[10]

BOHNER M, 2000, UNPUB OPIAL INEQUALI

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