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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... allow us to get away from the restriction that a map is bijective when we want to solve an equation. Indeed, the first natural instance when set- valued maps occur is the inverse f'1 of a single- valued map / from X to Y. We always ...
... mathematical economics and game theory started when von Neumann asked for an extension of the Brouwer Fixed Point Theorem to set-valued maps, which was needed for finding noncooperative equilibria for n- person games, for instance.
For instance, when we regard a set-valued map as a single- valued map from one set to the power set of the other (supplied with any one of the topologies we can think of) , we arrive at continuity concepts which are stronger than both ...
For instance, the concept of consistency is nothing other than the fact that the graph of F is the lower limit of the graphs of the approximate maps Fn, while stability is the boundedness of the inverses of the derivatives of the maps ...
But each of these extensions was devised for specific purposes (solving partial differential equations, for instance.) When we deal with real-valued functions, we are led to Properties of Set-Valued Maps 11 40441_11.pdf.