Set-Valued Analysis"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." —Mathematical Reviews "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." —Zentralblatt Math |
From inside the book
Results 1-5 of 59
... statements are quite different, two proofs are provided. This book presents only the tools, without mentioning applications. Some applications (to control theory and viability theory in particular) are presented in companion texts2 ...
... Statements of the Viability Theorems 389 10.1.3 Viability Kernels 392 10.1.4 Viability and Equilibria 393 10.2 Applications of the Viability Theorem 394 10.2.1 Linear Differential Inclusions 395 10.2.2 Lyapunov Functions 395 10.2.3 ...
... 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 such a problem, but also to ...
... 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 subset M satisfying ...
... statements If f(xn) converges in Y, then xn has a cluster point or i) f maps closed subsets to closed subsets ii) V compact M C Y, /_1(M) is compact { holds true. Proposition 1.2.3 We posit the assumptions of Proposition 1.2.2. Let us ...