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."
Results 1-5 of 71
3 Existence and Stability of an Equilibrium 77 3.1 Ky Fan's Inequality 80 3.2 Equilibrium and Fixed Point Theorems 83 3.2.1 The Equilibrium Theorem 83 3.2.2 Fixed Point Theorems 86 3.2.3 The Leray-Schauder Theorem 89 3.3 Ekeland's ...
Unilateral problems in mechanics were formulated in the framework of variational inequalities (also called "generalized equations" by some authors), which are again inclusions in disguise. Their solution by Stampacchia and J.-L. Lions ...
K'~ is the weak-* limit of a subsequence pni G K~, , inequalities < pn> , xn> > < 0 imply that < p, x >< 0. Conversely, assume that some x G ((J-Limsup^^ii:")- does not belong to the lower limit Liminfn^ooiirn.
... yn satisfying inequality \\x — xn|| < l\\y — yn\\ for n large enough. Hence x being the limit of xn € f~1(Mn) belongs to the lower limit of the inverse images of the subsets Mn. The proof of the second statement is analogous.
The latter allow characterization of closed convex subsets by an (infinite) family of linear inequalities thanks to a version of the Hahn-Banach Separation Theorem. It also enables one to deal with the class of upper semicontinuous ...