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."
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But whenever the proofs of the finite-dimensional and infinite- dimensional statements are quite different, two proofs are provided. This book presents only the tools, without mentioning applications. Some applications (to control ...
... Caratheodory Parametrization 376 9.7 Measurable/Lipschitz Parametrization 379 10 Differential Inclusions 383 10.1 The Viability Theorem 387 10.1.1 Solutions to Differential Inclusions 388 10.1.2 Statements of the Viability Theorems ...
We shall prove an equivalent statement, called the Equilibrium Theorem, which provides the existence of an equilibrium of a set-valued map, a solution to the inclusion F(x) 3 0. Of course, for applications, we need not only to solve ...
Proof — The first statement is obvious. The second one is a consequence of the following more general result: Proposition 1.1.5 Let us consider sequences of subsets Ln and Mn of a metric space and assume that there exists a compact ...
We recall that a continuous single-valued map from a metric space X to a metric space Y is proper if and only if one of the following equivalent statements If f(xn) converges in Y, then xn has a cluster point or i) f maps closed subsets ...