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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Jean-Pierre Aubin, Hélène Frankowska. P. DE FERMAT Epigraph Who needs set-valued analysis? Everyone, we are tempted to.
Epigraph Who needs set-valued analysis? Everyone, we are tempted to say, and we shall state our case. This strong conviction — born out of accumulated experience in using it in control theory and differential games, ...
... Extended Functions and their Epigraphs .... 222 6.1.2 Contingent Epiderivatives 224 6.1.3 Fermat and Ekeland Rules 232 6.1.4 Elementary Properties 234 6.2 Other Epiderivatives 236 6.2.1 Adjacent and Circatangent Epiderivatives .
142 4.4 The Menagerie of Tangent Cones: they may be all different 161 5.1 Graph of the Contingent Derivative 183 6.1 Epigraph of the Contingent Derivative 227 9.1 Approximate Selection of an Upper Semicontinuous Map359 9.2 Illustration ...
... with a function V the set-valued map Vj defined by VT(x) := [V(x),+oo[ whose graph is the epigraph of V. The graphs of the derivatives of such set-valued maps Vf are the epigraphs of functions which are called epiderivatives .