Handbook of Multivalued Analysis: Volume I: Theory / Edition 1 available in Hardcover
- Pub. Date:
- Springer US
This is the first of a two-volume exposition on the theory and applications of set-valued maps. Multivalued analysis is a remarkable mixture of many different fields of mathematics, such as topology, measure theory, nonlinear functional analysis and applied mathematics. This two-volume work provides a comprehensive survey of the general theory and applications of set-valued analysis. The existing books on the subject deal with either one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In contrast this volume gives a complete picture of the subject, including important new developments that occurred in recent years and a detailed bibliography. Although the presentation of the subject assumes some knowledge from various areas of mathematical analysis, the authors have made every effort, including the addition of an appendix, to keep the work self-contained.
Audience: The work is an essential reference for graduate students and researchers interested in multivalued analysis.
Table of Contents
Volume A: Theory.
1. Continuity of Multifunctions. 2. Measurable Multifunctions. 3. Monotone and Accretive Operators. 4. Degree Theory for Multifunctions. 5. Fixed Points. 6. Concave Multifunctions and Tangent Cones. 7. Convergence of Multifunctions. 8. Set-Valued Random Processes and Multimeasures. Appendix A.1. Topology. A.2. Measure Theory. A.3. Functional Analysis. References. Symbols. Index.