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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4.5.3 Hypertangent Cones 164 4.5.4 A Menagerie of Tangent Cones 165 4.6 Tangent Cones to Sequences of Sets 166 4.7 Higher Order Tangent Sets 171 5 Derivatives of Set- Valued Maps 179 5.1 Contingent Derivatives 181 5.2 Adjacent and ...
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 .
Introduction It is a fact that in mathematical sciences there has been a reluctance to deal with sequences of sets and set-valued maps. Despite the emergence of exciting new vistas for the applications of mathematics, ...
Taking into account uncertainties, disturbances, modeling errors, etc., leads naturally to set- valued maps and inclusions. They also arise when we wish to treat a problem qualitatively, by looking for solutions common to a set of data, ...
This unfortunate situation led to two concepts of semiconti- nuity of set-valued maps, introduced at the beginning of the thirties by Bouligand and Kuratowski: Lower and upper semi- continuity. These issues were developed in the ...