product iamge

Ulam stability of operators

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Download
Search on Amazon

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

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  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

Author(s): Brzdȩk, Janusz; Popa, Dorian; Rasa, Ioan; Xu, Bing et al.
Series: Mathematical analysis and its applications
Publisher: Elsevier
Year: 2018

Language: English
Pages: 228
Tags: Functional equations.;MATHEMATICS / Calculus.;MATHEMATICS / Mathematical Analysis.

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