Operator Inequalities, Volume 147 (Mathematics in Science and Engineering)

✍ Scribed by Schroder (editor)

• Publisher: Academic Press
• Year: 1980
• Tongue: English
• Leaves: 384
• Category: Library

✦ Table of Contents

Front Cover
Operator Inequalities
Copyright Page
Contents
Preface
Acknowledgments
Some remarks concerning notation
Chapter I. Some results on functional analysis
1. Basic concepts of order theory
2. Convex sets
3. Fixed-point theorems and other means of functional analysis
Notes
Chapter II. Inverse-positive linear operators
1. An abstract theory
2. M-matrices
3. Differential operators of the second order, pointwise inequalities
4. Abstract theory (continuation)
5. Numerical applications
6. Further Results
Notes
Chapter III. Two-sided bounds for second order differential equations
1. The concept of an inverse-monotone operator
2. Inverse-monotone differential operators
3. Inverse-rnonotonicity with weak differential inequalities
4. Existence and inclusion for two-point boundary Value Problems
5. Existence and inclusion by weak comparison functions
6. Error estimates
Notes
Chapter IV. An estimation theory for linear and nonlinear operators, range-domain implications
1. Sufficient conditions, general theory
2. Inverse-monotone operators
3. Inclusion by upper and lower bounds
4. Range–domain implications for linear and concave operators
Notes
Chapter V. Estimation and existence theory for vector-valued differential operators
1. Description of the problem, assumptions, notation
2. Two-sided bounds by range–domain implications
3. Existence and inclusion by two-sided bounds
4. Pointwise norm bounds by range–domain implications
5. Existence and estimation by norm bounds
6. More general estimates
Notes
References
Notation index
Subject index