پایداری اولام اپراتورها (تحلیل ریاضی و کاربردهای آن)

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, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations. Read more... Abstract: 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, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations Machine Generated Contents Note: 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 -- 2. Operators In Normed Spaces -- 1. 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 -- 6.1. Bernstein Operators -- 6.2. Szasz-mirakjan Operators -- 6.3. Other Classical Operators -- 6.4. Integral Operators -- 6.5. Bernstein-schnabl Operators -- References -- 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 Operator -- 6. Partial Differential Equations -- 7. Laplace Operator -- References -- 4. Best Constant In Ulam Stability -- 1. Introduction -- 2. Best Constant For Cauchy, Jensen, And Quadratic Functional Equations -- 3. Best Constant For Linear Operators -- 3.1. Stancu Operators -- 3.2. Kantorovich Operators -- 3.3. An Extremal Property Of K(bn) -- 4. Ulam Stability Of Operators With Respect To Different Norms -- References -- 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 Coefficients -- 6. Difference Equation With A Matrix Coefficient -- 7. Linear Functional Equations With Constant Coefficients -- 8. Linear Differential Equations -- 9. Integral Equations -- References -- 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. Authors, Janusz Brzdęk, Dorian Popa, Ioan Raşa, Bing Xu. Includes Bibliographical References And Index. Content: 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 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 spaces -- 1. 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 operator -- 6. 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 coefficients

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, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations.

• Allows readers to establish expert knowledge without extensive study of other books
• Presents complex math in simple and clear language
• Compares, generalizes and complements key findings
• Provides numerous open problems