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."
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Fermat also was the first to discover the "principle of least time" in optics, the prototype of the variational principles governing so many physical and mechanical laws. He shared independently with Descartes the invention of analytic ...
... Fixed Point Theorems 86 3.2.3 The Leray-Schauder Theorem 89 3.3 Ekeland's Variational Principle 91 3.4 Constrained Inverse Function Theorem 93 3.4.1 Derivatives of Single- Valued Maps 93 3.4.2 Constrained Inverse Function Theorems .
270 7.2 Convergence Theorems 270 7.3 Epilimits 274 7.3.1 Definitions and Elementary Properties 274 7.3.2 Convergence of Infima and Minimizers 281 7.3.3 Variational Systems 284 7.4 Epilimits of Sums and Composition Products 286 7.5 ...
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 ...
... 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 state some applications of the Viability Theorem.