Difference between revisions of "Book:Ravi Agarwal/Dynamic Inequalities on Time Scales"

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Latest revision as of 02:37, 20 December 2017

Ravi AgarwalDonal O'Regan and Samir Saker: Dynamic Inequalities on Time Scales


1 Preliminaries
1.1 Delta Calculus
1.2 Nabla Calculus
1.3 Diamond-$\alpha$ Calculus
1.4 Taylor Monomials and Series
2 Basic Inequalities
2.1 Young Inequalities
2.2 Jensen Inequalities
2.3 Hölder Inequalities
2.4 Minkowksi Inequalities
2.5 Steffensen Inequalities
2.6 Hermite-Hadamard Inequalities
2.7 Čebyšev Inequalities
3 Opial Inequalities
3.1 Opial Type Inequalities I
3.2 Opial Type Inequalities II
3.3 Opial Type Inequalities III
3.4 Higher Order Opial Type Inequalities
3.5 Diamond-$\alpha$ Opial Inequalities
4 Lyapunov Inequalities
4.1 Second Order Linear Equations
4.2 Second Order Half-Linear Equations
4.3 Second Order Equations with Damping Terms
4.4 Hamiltonian Systems
5 Halanay Inequalities
5.1 Shift Operators
5.2 Delay Functions Generated by Shift Operators
5.3 Halanay Inequality on Time Scales
5.4 Stability of Nonlinear Dynamic Equations
6 Wirtinger Inequalities
6.1 Wirtinger-Type Inequality I
6.2 Wirtinger-Type Inequality II
6.3 Further Wirtinger Inequalities
6.4 An Application of Wirtinger Inequalities on Time Scales