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 47
... Derivatives 215 6 Epiderivatives of Extended Functions 219 6.1 Contingent Epiderivatives 222 6.1.1 Extended Functions and their Epigraphs .... 222 6.1.2 Contingent Epiderivatives 224 6.1.3 Fermat and Ekeland Rules 232 6.1.4 Elementary ...
... Epiderivatives 300 8 Measurability and Integration of Set- Valued Maps 303 8.1 Measurable Set- Valued Maps 306 8.2 Calculus of Measurable Maps 310 8.3 Proof of the Characterization Theorem 319 8.4 Limits of Measurable Maps and ...
... derivative" of F at this point (x,y). Derivatives built in this way from the various choices of tangent cones are called graphical derivatives and the calculus of tangent cones can be transferred to a set-valued differential calculus ...
... derivatives introduced by Dini, who was among the first to revolt against the rigidity imposed by the heirs of Cauchy4. As far as optimization is concerned, the Fermat Rule can be extended to any function by using these epiderivatives ...
... epiderivatives, can even be taken lower semicontinu- ous), relate the graphical derivatives of the solution map to the solution map of variational inclusions (which are linearizations of the differential inclusion along a solution) and ...