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 54
... elements xn € Kn, and the upper limit is the set of cluster points of such sequences. We mentioned already that stability is the only requirement that we retain to study ill posed or inverse problems. Stability is a catch word which ...
... elements xn € Kn and the upper limit is the set of cluster points of such sequences. Some elementary properties of lower and upper limits are investigated in Section 1, whereas their calculus is presented in Section 2. Set- valued maps ...
... elements xn G Kn has a cluster point.) Concerning sequences of singleta {xn}, the set limit, when it exists, is either empty (the sequence of elements xn is not converging), or is a singleton made of the limit of the sequence. It is ...
... xn € B(Kn,e) Remark — Replacing the balls of a metric space by neighborhoods ... elements of K has a cluster point. (See for instance [148, Section 1.7] ... elements of and the lower limit is the set of limits of such generalized sequences ...
... elements xn € Kn is the sequentially weak upper limit of the subsets Kn. In this way, we can present lower and upper limits in the framework of metric spaces or of (countable) sequences, leaving to the interested reader the task of ...