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 81
... denote by dx(x) := d(x,K) :— inf d(x,y) y&K 2These concepts should not be confused with the upper and lower semicontinuity of real- valued functions. the distance from x to K, where we set d(x, 16 Continuity of Set-Valued Maps 40441_16.pdf.
... denoted by Bx{K,r) := {xeX \ d(x,K)<r} When there is no ambiguity, we set B(K,r) := Bx(K,r) When X is a Banach space whose unit ball is denoted by B (or Bx if the space must be mentioned) , we observe that Bx(K,r) = K + rBx The balls B ...
... denoted by X*. We say that the bilinear map < •, • > (p,x) e X* x X h->< p,x > := p(x) is the duality pairing. We recall that the weakened topology cr(X, X*) of X is defined by the semi-norms Pm(x) := sup | < q,x > | qeM when M := {qi ...
... denote by Af" the upper limit of the Mn and 1} the lower limit of the Ln. Then limsupn^oo ( sup inf tp(z,y)\ < sup inf <p(z, y) \yeMn *€Ln / y€M» *€Lb Proof — Let y belong to M". Since tp is upper semicontinuous, we know that for any ...
... denote the sequentially weak upper limit of the polar cones K~ . Theorem 1.1.8 Let (Kn)ne-^ be a sequence of closed ... denoted (Kn)ne^) sucn that V n > 0, (x + eB) D Kn = 0 The Separation Theorem implies the existence of elements pn G X ...