Operator inequalities / Johann Schröder.

Includes bibliographical references (pages 343-357) and indexes.

Print version record.

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 equations1. 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 operatorsNotes; 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

eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - Worldwide