Handbook of Multivalued Analysis

Volume I: Theory
1997. Auflage 1997
ISBN: 978-0-7923-4682-1
Verlag: Springer Us

Buch, Englisch, 968 Seiten, Format (B × H): 155 mm x 234 mm, Gewicht: 1474 g

Reihe: Mathematics and Its Applications

the many different applications that this theory provides. We mention that the existing literature on this subject includes the books of J. P. Aubin, J. P. Aubin-A. Cellina, J. P. Aubin-H. Frankowska, C. Castaing-M. Valadier, K. Deimling, M. Kisielewicz and E. Klein-A. Thompson. However, these books either deal with one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In this volume, we have tried very hard to give a much more complete picture of the subject, to include some important new developments that occurred in recent years and a detailed bibliography. Although the presentation of the subject requires some knowledge in various areas of mathematical analysis, we have deliberately made this book more or less self-contained, with the help of an extended appendix in which we have gathered several basic notions and results from topology, measure theory and nonlinear functional analysis. In this volume we present the theory of the subject, while in the second volume we will discuss mainly applications. This volume is divided into eight chapters. The flow of chapters follows more or less the historical development of the subject. We start with the topological theory, followed by the measurability study of multifunctions. Chapter 3 deals with the theory of monotone and accretive operators. The closely related topics of the degree theory and fixed points of multifunctions are presented in Chapters 4 and 5, respectively.

Zielgruppe

Research

Autoren/Hrsg.

Papageorgiou, Nikolaos S

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.