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 61
... called "generalized equations" by some authors), which are again inclusions in disguise. Their solution by Stampacchia and J.-L. Lions in the sixties gave a new impetus to set-valued maps, with a different vocabulary. 5. Set- valued ...
... called the marginal (or performance or value) function. For every y G Y, let G(y) := {x€X\W(x,y) = V(y)} be the subset of solutions to our minimization problem. One of the main issues of optimization theory is to study the set-valued ...
... called the graphical approach.) For instance, closed maps, that is maps with closed graph, shall play a starring role in this book. It is a weaker property than continuity or even, upper semicontinuity, very familiar and thus easy 6 ...
... (called linear processes.) This generalization is not bold enough, since dealing exclusively with closed vector subspaces is still too restrictive: We need to use the notion of closed convex cone, which is a kind of vector subspace in ...
... called the Equilibrium Theorem, which provides the existence of an equilibrium of a set-valued map, a solution to the inclusion F(x) 3 0. Of course, for applications, we need not only to solve such a problem, but also to approximate its ...