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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Newton himself recognized explicitly that he got the hint of the differential calculus from Fermat 's method of building tangents devised half a century earlier. This same method is used in our book to build a differential calculus for ...
This strong conviction — born out of accumulated experience in using it in control theory and differential games, mathematical economics and game theory, biomathematics, qualitative physics and viability theory — led us to devote time ...
... Maps • Measures and Integration • Differential Equations The set-valued version of this list is nothing other than the outline of this book. Our account of set-valued analysis is by no means exhaustive: it is just an introduction.
We did not restrict our exposition to the framework of finite dimensional vector-spaces, since set- valued analysis is also useful for solving problems involving partial differential equations or inclusions. But whenever the proofs of ...
... and Elementary Properties 189 5.2.2 Limits of Differential Quotients 191 5.2.3 Derivatives of monotone operators 194 5.3 Chain Rules 196 5.4 Inverse Set- Valued Map Theorem 203 5.4.1 Stability and Approximation of Inclusions .