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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Requiring that maps should be always single-valued, and even bijective, is too costly an attitude, above all in many applied fields, where we are not free to make such assumptions. This was indeed recognized during the three first ...
In view of such a wide variety of motivating applications, it is fortunate that most of the basic results of the chapters of "single- valued" analysis can be adapted to the set-valued realm. These include: • Limits and Continuity ...
... Fixed Point Theorems 86 3.2.3 The Leray-Schauder Theorem 89 3.3 Ekeland's Variational Principle 91 3.4 Constrained Inverse Function Theorem 93 3.4.1 Derivatives of Single- Valued Maps 93 3.4.2 Constrained Inverse Function Theorems .
Despite the emergence of exciting new vistas for the applications of mathematics, our long familiarity with sequences (of elements) and with (single-valued) maps has perhaps been so deeply rooted in traditional mathematical ...
The (single-valued) map / describes the dynamics of the system: It associates with the state x of the system and the control u the velocity f(x, u) of the system. The set- valued map U describes a feedback map assigning to the state x ...