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 6-10 of 52
... problems where uniqueness of the solution is naturally lacking : Let W be a function from X x Y to R. We consider the family of minimization problems VyЄY , V ( y ) : = inf W ( x , y ) xЄX parametrized by parameters y . The function V ...
... problems ; The Pontriagin principle when dealing with optimal control problems . After the advances of Functional Analysis , it was time to un- cover the common fact behind all these results . It is still and always the Fermat rule ...
... problems . Stability is a catch word which means that the set of solutions depends continuously upon the data . How can we proceed to define continuity of set - valued maps ? If we try to adapt to the set - valued case the two ...
... line with Hadamard's linearity bill enforced by Fréchet that a derivative should be linear with respect to the increment . • NONLINEAR FUNCTIONAL ANALYSIS We are convinced that many problems. Properties of Set - Valued Maps 7 40441_7.pdf.
... problem , but also to approximate its solutions by solutions to approximate problems : given Fn : Xn → Yn , yn Є Yn , find în Є Xn with Fn ( xn ) ⇒ Yn where Xn and Yn are subspaces of X and Y. The famous Lax's principle of numerical ...