Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student."
—The Journal of the Indian Institute of Science
"The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis."
"I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject."
—Bulletin of the American Mathematical Society
"This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis."
Results 1-5 of 73
Contents Introduction 1 1 Continuity of Set- Valued Maps 15 1.1 Limits of Sets 16 1.1.1 Definitions 16 1.1.2 The ... of Closed Convex Process 67 2.6 Upper Hemicontinuous Maps 74 3 Existence and Stability of an Equilibrium 77 3.1 Ky.
9 Selections and Parametrization 353 9.1 Case of lower semicontinuous maps 355 9.2 Case of upper semicontinuous maps 358 9.3 Minimal ... Comments 411 Bibliography 421 Index 457 List of Figures 1.1 Example of Upper and Lower Limits xvii.
List of Figures 1.1 Example of Upper and Lower Limits of Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and Maximal Monotone Maps .
Limits and Continuity Limits of sets were introduced by Painleve in the first years of this century, ... The lower limit of a sequence of subsets Kn is the set of limits of sequences of elements xn € Kn, and the upper limit is the set ...
... introduced at the beginning of the thirties by Bouligand and Kuratowski: Lower and upper semi- continuity. ... we shall start this book with the study of limits and leave aside the examination of topologies on power sets.