## 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 35

By Bouligand, with the notions of contingent and paratingent, by Dini who also broke Hadamard's linearity law, by L. Schwartz and S. Sobolev, with the discovery of

**weak**derivatives of functions and distributions.

We may need the above extension when dealing with

**weak**topologies of a Banach space X and of its dual denoted by X*. We say that the bilinear map < •, • > (p,x) e X* x X h->< p,x > := p(x) is the duality pairing.

The key facts that can be recalled now are that X* is still the dual of X supplied with the weakened topology, that X is the dual of X* supplied with the

**weak**-* topology, and that the bounded subsets of the dual X* are weakly relatively ...

We introduce the (negative) polar cones to subsets K C X and LcX* denned by K~ := {pe X* | Vx G <p,a:>< 0} and L~ := {i€l| VpeL, <p,x>< 0} Let it — Limsupjj^ooiiL" denote the sequentially

**weak**upper limit of the polar cones K~ .

Let us consider a sequence xn € Kn such that a subsequence of elements A(xn) (again denoted A(xn)) converges weakly to some y in Y. We shall check that (£n)neN has a

**weak**cluster point, by showing that it is weakly bounded, and thus, ...

### What people are saying - Write a review

sss