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 51
The crucial revolution in the history of the concept of gradients happened in the sixties when J.- J. Moreau and R. T. Rock- afellar proposed in the framework of convex analysis the notion of subdifferential of a convex function, ...
Limits and Continuity Limits of sets were introduced by Painleve in the first years of this century, just after Frechet axiomatized in 1906 the concept of £-spaces (on which a notion of limit is defined2.) Studying limits of sets ...
This unfortunate situation led to two concepts of semiconti- nuity of set-valued maps, introduced at the beginning of the thirties by Bouligand and Kuratowski: Lower and upper semi- continuity. These issues were developed in the ...
For instance, the concept of consistency is nothing other than the fact that the graph of F is the lower limit of the graphs of the approximate maps Fn, while stability is the boundedness of the inverses of the derivatives of the maps ...
Tangents and Normals The concept of tangency has been overshadowed in some sense by the requirement that the space of tangent vectors must be a vector space, so that the original idea became concealed after its formal implementation in ...