Set-Valued Analysis"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." —Mathematical Reviews "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." —Zentralblatt Math |
From inside the book
Results 1-5 of 80
... image of being something difficult and mysterious and, consequently, was regarded as a mathematical curiosity, to be left in the hands of mathematicians who like to generalize for the sake of generalizing, without proper motivations. In ...
... 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 ... 46 1.4.4 Marginal Maps 48 1.5 Lower Semi ...
... Image 146 4.3.2 Example: Tangent cones to subsets defined by equality and inequality constraints 150 4.3.3 Direct Image 153 4.4 Normal Cones 156 4.5 Other Tangent Cones 159 4.5.1 Convex Kernel of a Cone 159 4.5.2 Paratingent Cones 160 ...
... 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 Epiderivatives 222 6.1.1 Extended Functions ...
... images of the set- valued map must be convex. Actually, a Lipschitz set- valued map F with closed convex images is parametrizable in the sense that there exists a "control space" U and a Lipschitz map / : X x U i— ▻ X such that Vx, F{x) ...