Book:Ravi Agarwal/Dynamic Inequalities on Time Scales

Ravi Agarwal, Donal O'Regan and Samir Saker: Dynamic Inequalities on Time Scales

Contents

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

Bibliography

Index