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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One can no longer afford the luxury of studying only well posed problems in Hadamard's sense: /// posed problems, inverse problems and many other unorthodox problems under other names are popping up in every domain of activity, ...
... 1.2 Calculus of Limits 27 1.2.1 Direct Images 28 1.2.2 Inverse Images 30 1.3 Set- Valued Maps 33 1.4 Continuity of Set- Valued maps 38 1.4.1 Definitions 38 1.4.2 Generic Continuity 44 1.4.3 Example: Parametrized Set- Valued Maps .
... 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 .
203 5.4.2 Localization of Inverse Images 206 5.4.3 The Equilibrium Map 207 5.4.4 Local Injectivity 209 5.5 Qualitative Solutions 210 5.6 Higher Order Derivatives 215 6 Epiderivatives of Extended Functions 219 6.1 Contingent ...
List of Figures 1.1 Example of Upper and Lower Limits of Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and Maximal Monotone Maps .