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 6-10 of 78
... solution to the inclusion F ( x ) ⇒ 0 . Of course , for applications , we need not only to solve such a problem , but also to approximate its solutions by solutions to approximate problems : given Fn : Xn → Yn , yn Є Yn , find în Є Xn ...
... solutions to equations with constraints . They also appear in the formu- lation of necessary conditions in optimization problems with constraints and play a key role in viability theory . In order to define space of normals , which in ...
... solution to a differential equation or inclusion ( Lyapunov property . ) The set - valued approach indicates the route : We associate with a function V the set - valued map V ↑ defined by V1 ( x ) = [ V ( x ) , + ∞ [ whose graph is ...
... solution . Hence , we cannot escape the burden of studying measurable maps , which are the maps whose graphs are measurable , and checking in particular that all the standard operations preserve measurability . We also need ...
... solution map to the solution map of variational inclusions ( which are linearizations of the differential inclusion along a solution ) and state some applications of the Viability Theorem . SELECTIONS AND PARAMETRIZATION We cannot ...