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 87
The second one is a consequence of the following more general result: Proposition 1.1.5 Let us consider sequences of subsets Ln and Mn of a metric space and assume that there exists a compact subset M satisfying the following property: ...
For m — 0, we set Kn^ '□= Kn. Assume that the m — 1 first subsequences , 0 < p < m — 1 have been constructed. Consider the mth open subset Um. Then either for every subsequence Uj, ^□(Limsup^X^-1)) ^ 0 in which case we set K^1 ...
K'~ is the weak-* limit of a subsequence pni G K~, , inequalities < pn> , xn> > < 0 imply that < p, x >< 0. Conversely, assume that some x G ((J-Limsup^^ii:")- does not belong to the lower limit Liminfn^ooiirn.
Let us assume that f is proper, then /(Limsup^^Kn) = Limsup n— >oo f(Kn) Furthermore, if f is surjective, we obtain f~l (Limsupn_+00Mn) = Limsupn_>0O/_1(Mn) The proof is a simple consequence of definitions and is omitted.
Proposition 1.2.5 Let us consider two Banach spaces X and Y , a continuous linear operator A G C(X, Y) and a sequence of convex subsets Mn C Y. We assume that the "constraint qualification assumption" 3 7 > 0, c> 0 such that jB C cA(Bx) ...