| Description |
1 online resource (x, 256 pages) |
| Contents |
880-01 Preliminaries -- Basic Inequalities -- Opial Inequalities -- Lyapunov Inequalities -- Halanay Inequalities -- Wirtinger Inequalities |
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880-01/(S Machine generated contents note: 1. Preliminaries -- 1.1. Delta Calculus -- 1.2. Nabla Calculus -- 1.3. Diamond-α Calculus -- 1.4. Taylor Monomials and Series -- 2. Basic Inequalities -- 2.1. Young Inequalities -- 2.2. Jensen Inequalities -- 2.3. Holder Inequalities -- 2.4. Minkowski Inequalities -- 2.5. Steffensen Inequalities -- 2.6. Hermite--Hadamard Inequalities -- 2.7. Cebysev 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-α Opial Inequalities -- 4. Lyapunov Inequalities -- 4.1. Second Order Linear Equations -- 4.2. Second Order Half-Linear Equation -- 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. Application of Wirtinger Inequalities on Time Scales |
| Summary |
This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail |
| Analysis |
wiskunde |
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mathematics |
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functionaalanalyse |
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functional analysis |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed November 19, 2014) |
| Subject |
Inequalities (Mathematics)
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Time-series analysis.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Inequalities (Mathematics)
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Time-series analysis
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| Form |
Electronic book
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| Author |
O'Regan, Donal, author.
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Saker, Samir, author
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| ISBN |
9783319110028 |
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3319110020 |
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3319110012 |
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9783319110011 |
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