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
Results 1-5 of 81
... Banach- Steinhaus Theorem, can be adapted to closed convex processes. The first one states that a closed convex process defined on the whole space ... spaces and cones. They truly deserve the status of linear set- valued maps. 3keeping us in ...
... Banach space whose unit ball is denoted by B (or Bx if the space must be mentioned) , we observe that Bx(K,r) = K + rBx The balls B(K,r) are neighborhoods of K. When K is compact, each neighborhood of K contains such a ball around K ...
... space by neighborhoods and the sequences of a metric space by generalized sequences, we can extend the concepts of ... Banach space X and of its dual denoted by X*. We say that the bilinear map < •, • > (p,x) e X* x X h->< p,x > := p(x) ...
... Banach space X*, endowed with the norm ||p||* := sup | <p,x > | IWI<i The space X is called reflexive if X = X**. In this case, it enjoys both the properties of a Banach space and of the dual of a Banach space, including the weak ...
... Banach space X. Then Liminfn^ooKn = (a - Limsupn^0C)ii'r;)_ Proof — Inclusion Liminfn^ooiirn C (a - Limsupn^0O.fi:j7)_ is obvious: If x G Liminfn_>00.K„ is the limit of a sequence of elements xn € Kn and p € a - Limsupn_00.K'~ is the ...