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."
Introduction It is a fact that in mathematical sciences there has been a reluctance to deal with sequences of sets and set-valued maps.
Taking into account uncertainties, disturbances, modeling errors, etc., leads naturally to set- valued maps and inclusions. They also arise when we wish to ...
One of the main issues of optimization theory is to study the set-valued map G (nonvacuity, continuity and differentiability in a suitable sense, and so on.) ...
This unfortunate situation led to two concepts of semiconti- nuity of set-valued maps, introduced at the beginning of the thirties by Bouligand and ...
For example, this is the case for the Brouwer Fixed Point Theorem, whose generalization to set-valued maps is the famous Kakutani Fixed-Point Theorem.