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."
Results 1-5 of 94
46 1.4.4 Marginal Maps 48 1.5 Lower Semi-Continuity Criteria 49 2 Closed Convex Processes 55 2.1 Definitions 56 2.2 Open Mapping and Closed Graph Theorems 57 2.3 Uniform Boundedness Theorem 61 2.4 The Bipolar Theorem 62 2.5 ...
... Stability Conditions 101 3.4.4 Local Uniqueness 103 3.5 Monotone and Maximal Monotone Maps 104 3.5.1 Monotone Maps 104 3.5.2 Maximal Monotone Maps 106 3.5.3 Yosida Approximations Ill 3.6 Eigenvectors of Closed Convex Processes 114 4 ...
6.6.1 Second Order Epiderivatives of Moreau-Yosida Approximations 263 7 Graphical & Epigraphical Convergence 265 7.1 Graphical Limits 267 7.1.1 Definitions 267 7.1.2 Graphical Convergence of Closed Convex Processes 269 7.1.3 Monotone ...
For this reason, we select the closed convex processes, i.e., the maps whose graphs are closed convex cones, as the candidates to play the part of set- valued linear maps. We shall see later that derivatives of some set-valued maps are ...
Some of these tangent cones are closed convex cones, and they enjoy a property which is the natural extension of linearity (without subtraction.) These tangent cones possess a rich calculus which justifies their use in many questions, ...