## 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 94

... 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 ... 125 4.1.3 Adjacent and Clarke Tangent Cones 126 4.1.4 Sleek

**Subsets**130 4.1.5 Limits of Contingent Cones; ...

Furthermore, we shall renew history, by regarding a map not ... as a map, but as a graph (a

**subset**of the product of the departure ... For instance,

**closed**maps, that is maps with

**closed**graph, shall play a starring role in this book.

If we come back to the idea underlying the notion of tangency to a

**subset**K at some point x € K, we are tempted to form "thick" differential ... We obtain in this way a variety of

**closed**cones made of what we call tangent vectors.

... for any set-valued map F, since we have introduced a way to implement the tangency for any

**subset**of a normed space. ... The latter involving

**closed**convex processes, this strategy provides ways for transferring some properties of ...

It happens that set-valued maps with

**closed**graph taking their values in a compact set are upper semicontinuous. ... When K is a

**subset**of X, we denote by dx(x) := d(x,K) :— inf d(x,y) y&K 2These concepts should not be confused with the ...

### What people are saying - Write a review

sss