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
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... equations , when dealing with prob- lems of the calculus of variations ; Lagrange and Kuhn - Tucker multipliers , when state con- straints were added to optimization problems ; The Pontriagin principle when dealing with optimal control ...
... equations can be extended to the case of inclusions . For example , this is the case for the Brouwer Fixed Point The- orem , whose generalization to set - valued maps is the famous Kakutani Fixed - Point Theorem . We shall prove an ...
... 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 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 the epigraph of V. The graphs ...
... . But each of these extensions was devised for specific purposes ( solving partial differential equations , for instance . ) When we deal with real - valued functions , we. Properties of Set - Valued Maps 11 40441_11.pdf.