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Ulam stability of operators /
Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London, United Kingdom :
Academic Press,
[2018]
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| Colección: | Mathematical analysis and its applications.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Ulam Stability of Operators; Copyright; Dedication; Contents; Acknowledgment; Preface; About the Authors; CHAPTER 1: Introduction to Ulam stability theory; 1. Historical background; 2. Stability of additive mapping; 3. Approximate isometries; 4. Other functional equations and inequalities in several variables; 5. Stability of functional equations in a single variable; 6. Iterative stability; 7. Differential and integral equations; 8. Superstability and hyperstability; 9. Composite type equations; 10. Nonstability; References
- CHAPTER 2: Ulam stability of operators in normed spaces1. Introduction; 2. Ulam stability with respect to gauges; 3. Closed operators; 4. Some differential operators on bounded intervals; 5. Stability of the linear differential operator with respect to different norms; 6. Some classical operators from the approximation theory; References; CHAPTER 3: Ulam stability of differential operators; 1. Introduction; 2. Linear differential equation of the first order; 3. Linear differential equation of a higher order with constant coefficients; 4. First-order linear differential operator
- 5. Higher-order linear differential operator6. Partial differential equations; 7. Laplace operator; References; CHAPTER 4: Best constant in Ulam stability; 1. Introduction; 2. Best constant for Cauchy, Jensen, and Quadratic functional equations; 3. Best constant for linear operators; 4. Ulam stability of operators with respect to different norms; References; CHAPTER 5: Ulam stability of operators of polynomial form; 1. Introduction; 2. Auxiliary results; 3. A general stability theorem; 4. Complementary results for the second-order equations
- 5. Linear difference equation with constant coefficients6. Difference equation with a matrix coefficient; 7. Linear functional equations with constant coefficients; 8. Linear differential equations; 9. Integral equations; References; CHAPTER 6: Nonstability theory; 1. Preliminary information; 2. Possible definitions of nonstability; 3. Linear difference equation of the first order; 4. Linear difference equation of a higher order; 5. Linear functional equation of the first order; 6. Linear functional equation of a higher order; References; Index; Back Cover