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Handbook of Multivalued Analysis : Handbook of Multivalued Analysis Theory v. 1 - Shouchuan Hu

Handbook of Multivalued Analysis

Handbook of Multivalued Analysis Theory v. 1

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Published: 1st October 1997
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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.

Theory
Continuity of Multifunctions
Measurable Multifunctions
Monotone and Accretive Operators
Degree Theory for Multifunctions
Fixed Points
Concave Multifunctions and Tangent Cones
Convergence of Multifunctions
Set-Valued Random Processes and Multimeasures
Appendix A.1
Topology. A.2
Measure Theory. A.3
Functional Analysis
References
Symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792346821
ISBN-10: 0792346823
Series: Mathematics and Its Applications : Book 1
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 968
Published: 1st October 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 5.72
Weight (kg): 1.68