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."
Results 1-5 of 49
It is possible to implement this idea for any set-valued map F, since we have introduced a way to implement the tangency for any subset of a normed space. Therefore, in the framework of a given problem, we can regard a tangent cone to ...
1.1.4 Convex Hull of Limits Since the distance function to a subset of a normed space is convex if and only if this subset is convex, we infer that the lower limit of a sequence of convex subsets is closed and convex.
... some of them being adaptations of results on lower limits of sequences to the continuous case. Proposition 1.5.1 Consider a metric space X, two normed spaces Y and Z, two set-valued maps G and F from XtoY and Z respectively, ...
Proposition 1.5.2 Consider a metric space X, two normed spaces Y and Z, two set-valued maps G and F from XtoY and Z respectively and a (single-valued) map f from XxZtoY such that i) F is lower semicontinuous with convex values ii) f is ...
... set-valued map is still lower semicontinuous. □ We extend now the above lower semicontinuity criterion to infinite intersection of set- valued maps. Theorem 1.5.3 Let us consider a metric space X, normed vector- spaces Y and Z and ...