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."
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List of Figures 1.1 Example of Upper and Lower Limits of Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and Maximal Monotone Maps .
Furthermore, we shall renew history, by regarding a map not ... as a map, but as a graph (a subset of the product of ... P. de Fermat and R. Descartes, before the concept of function and map evolved from the one of curves and graphs.
Remembering that the graph of a continuous linear operator is a closed vector subspace, we are tempted to single out the maps whose graphs are closed linear subspaces (called linear processes.) This generalization is not bold enough, ...
For instance, the concept of consistency is nothing other than the fact that the graph of F is the lower limit of the graphs of the approximate maps Fn, while stability is the boundedness of the inverses of the derivatives of the maps ...
The idea is very simple and goes back to the prehistory of the differential calculus, when Pierre de Fermat introduced in the first half of the seventeenth century the concept of tangent to the graph of a function: The tangent space to ...