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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Newton himself recognized explicitly that he got the hint of the differential calculus from Fermat 's method of building tangents devised half a century earlier. This same method is used in our book to build a differential calculus for ...
This was indeed recognized during the three first decades of this century by the founders of "Functional Calculus": Painleve, Hausdorff, Bouligand, Kuratowski to quote only a few. In his important book Topologie, Kuratowski gave ...
Jean-Pierre Aubin Helene Frankowska Paris September 21, 1989 2Viability Theory  by Aubin, and the forthcoming books Set- Valued Analysis and Control Theory  by Frankowska and Set- Valued Analysis and Subdifferential Calculus ...
Contents Introduction 1 1 Continuity of Set- Valued Maps 15 1.1 Limits of Sets 16 1.1.1 Definitions 16 1.1.2 The Compactness Theorem 23 1.1.3 The Duality Theorem 24 1.1.4 Convex Hull of Limits 26 1.2 Calculus of Limits 27 1.2.1 Direct ...
... Finite Dimensional Case 130 4.1.6 Limits of Contingent Cones; Infinite Dimensional Case 132 4.2 Tangent Cones to Convex Sets 138 4.3 Calculus of Tangent Cones 146 4.3.1 Intersection and Inverse Image 146 4.3.2 Example: Tangent cones ...