Handbook of Multivalued Analysis: Volume I: Theory

by Shouchuan Hu, Nikolaos S. Papageorgiou

Overview

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.

Product Details

ISBN-13:	9780792346821
Publisher:	Springer US
Publication date:	10/31/1997
Series:	Mathematics and Its Applications , #419
Edition description:	1997
Pages:	968
Product dimensions:	6.10(w) x 9.25(h) x (d)

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.

Editorial Reviews

The first in a two-volume comprehensive survey of the field that combines topology, measure theory, nonlinear functional analysis, and applied mathematics. Following more or less the history of the subject, covers the continuity of multifunctions, measurable multifunctions, monotone and accretive operators, degree theory for multifunctions, fixed points, concave multifunctions and tangent cones, the convergence of multifunctions, and set-valued random processes and multimeasures. The second volume (unseen) describes applications. Readers are assumed to be graduate students or researchers with some knowledge of the various areas of mathematical analysis, but appendices review the appropriate topology, measure theory, and functional analysis. Annotation c. by Book News, Inc., Portland, Or.

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