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 39
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 ...
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 ...
Chapter 2 Closed Convex Processes Introduction Naturally, the first question which arises is: What are the set- valued analogues of continuous linear operators? Since the graph of a continuous linear operator A € C(X, Y) is a (closed) ...
closed convex process is given in this section for linear processes and in Chapter 4 (Section 2) in the general case. We shall also provide in Chapter 3 a theorem on existence of eigenvectors of closed convex processes (Theorem 3.6.2.) ...
The main examples of closed processes are provided by contingent derivatives of set-valued maps that we shall introduce in Chapter 5. We associate with a closed convex process its norm defined in the following way.