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" Ulam stability of operators / "
authors, Janusz Brzdęk, Dorian Popa, Ioan Raşa, Bing Xu.
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BL
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| Record Number
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872377
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| Main Entry
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Brzdȩk, Janusz
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| Title & Author
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Ulam stability of operators /\ authors, Janusz Brzdęk, Dorian Popa, Ioan Raşa, Bing Xu.
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| Publication Statement
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London, United Kingdom :: Academic Press,, [2018]
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| Series Statement
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Mathematical analysis and its applications
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| Page. NO
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1 online resource.
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| ISBN
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0128098309
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: 9780128098301
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0128098295
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9780128098295
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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
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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
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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
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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
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| Abstract
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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.
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| Subject
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Functional equations.
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Functional equations.
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MATHEMATICS / Calculus.
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| Subject
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MATHEMATICS / Mathematical Analysis.
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| Dewey Classification
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515/.45
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| LC Classification
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QA431
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| Added Entry
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Popa, Dorian
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Rasa, Ioan
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Xu, Bing
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