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 was also the one who discovered that the derivative of a (polynomial) function vanishes when it reaches an extremum. (This is Fermat's Rule, which remains the main strategy for obtaining necessary conditions of op- timality, ...
... 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 .
4.5.3 Hypertangent Cones 164 4.5.4 A Menagerie of Tangent Cones 165 4.6 Tangent Cones to Sequences of Sets 166 4.7 Higher Order Tangent Sets 171 5 Derivatives of Set- Valued Maps 179 5.1 Contingent Derivatives 181 5.2 Adjacent and ...
... Inclusion 398 10.3 Nonlinear Semi-Groups 399 10.4 Filippov's Theorem 400 10.5 Derivatives of the Solution Map 403 Bibliographical Comments 411 Bibliography 421 Index 457 List of Figures 1.1 Example of Upper and Lower Limits xvii.
142 4.4 The Menagerie of Tangent Cones: they may be all different 161 5.1 Graph of the Contingent Derivative 183 6.1 Epigraph of the Contingent Derivative 227 9.1 Approximate Selection of an Upper Semicontinuous Map359 9.2 Illustration ...