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 77
... Monotone Maps 106 3.5.3 Yosida Approximations Ill 3.6 Eigenvectors of Closed Convex Processes 114 4 Tangent Cones 117 4.1 Tangent Cones to a Subset 121 4.1.1 Contingent Cones 121 4.1.2 Elementary Properties of Contingent Cones .
104 4.1 Contingent Cone at a Boundary Point may be the Whole Space 122 4.2 The Graph of T[aM (•) 123 4.3 ... Properties of Contingent Cones 124 4.2 Properties of Adjacent Tangent Cones 129 4.3 Properties of Tangent Cones to Convex Sets ...
These cones enjoy many properties of the vector subspaces. 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.
The most popular of these tangent cones is for the time the contingent cone introduced in the thirties by Bouligand, ... Some of these tangent cones are closed convex cones, and they enjoy a property which is the natural extension of ...
Therefore, in the framework of a given problem, we can regard a tangent cone to the graph of the set-valued map F at some ... The latter involving closed convex processes, this strategy provides ways for transferring some properties of ...