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 88
... 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 . . 125 4.1.3 Adjacent and Clarke Tangent Cones 126 4.1.4 Sleek Subsets 130 4.1 ...
... subset K at some point x € K, we are tempted to form "thick" differential ... closed convex cones, and they enjoy a property which is the natural ... subset. • Differentiation of Maps We already mentioned that the concept of stability in ...
... set limit. If not, there would exist xo € Limsup^oo ... closed convex cones Kn, upper limits and lower limits can be exchanged by duality. We introduce the (negative) polar cones to subsets K C 24 1 - Continuity of Set-Valued Maps 40441_24.
... 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~ . Theorem 1.1.8 Let (Kn)ne-^ be a sequence of closed ...
... convex, we infer that the lower limit of a sequence of convex subsets is closed and convex. It is useful to have a ... subsets Kn contained in a bounded subset of a finite dimensional vector space X. Then co (Limsup^oo-Kn) = f] co I (J ...