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
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... problems in Hadamard's sense: /// posed problems, inverse problems and many other unorthodox problems under other names are popping up in every domain of activity, whenever the existence of a solution may fail for some data, whenever ...
... problems arising in other fields of knowledge — control theory, economics and management, biology and systems sciences, artificial intelligence, etc. — was pressing enough to help mathematicians overcome the kind of recalcitrance felt ...
... problems involving partial differential equations or inclusions. 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 ...
... problems or some simple underlying structure in order to avoid set- valued maps. For this reason, we begin by providing examples of natural and/or general problems involving set-valued maps before giving a rough description of the ...
... Problems with constraints also yield specific set-valued maps: Solving the equation f(x) = y, where the solution x is required to belong to a subset K, amounts to solving the inclusion f\x{x) = y where the restriction of / to K, is ...