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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... the invention of analytic geometry and with Pascal the creation of the mathematical theory of probability. His achievements in number theory overshadowed his other contributions, and the Last Fermat Theorem remains a challenge.
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 ...
In contrast, as it turned out, the need for set- valued analysis in solving problems arising in other fields of knowledge — control theory, economics and management, biology and systems sciences, artificial intelligence, etc.
by our experience in applying these results in control and viability theory. However, we tried very hard to make this presentation as clear as possible, to help the reader become familiar with the main tools.
... provide a useful framework for control theory, since the early contributions of Wazewski and Filippov in the beginning of the sixties. Such set- valued maps, called parametrized maps, are associated with a family of maps x i— > f(x, ...