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 82
... solution may fail for some data, whenever uniqueness of the solution is at stake. Requiring that maps should be always single-valued, and even bijective, is too costly an attitude, above all in many applied fields, where we are not free ...
... Solutions to Differential Inclusions 388 10.1.2 Statements of the Viability Theorems 389 10.1.3 Viability Kernels 392 ... Solution Map 403 Bibliographical Comments 411 Bibliography 421 Index 457 List of Figures 1.1 Example of Upper and ...
... solution or its uniqueness is not guaranteed for some data: Set-valued maps allow us to get away from the ... solutions f-\y) := {xeX\f(x) = y} to the equation f(x) = y. Of the three commandments of Hadamard's tablets, existence ...
... solution x is required to belong to a subset K, amounts to solving the inclusion f\x{x) = y where the restriction of / to K, is regarded as the set-valued map associating with x the point f(x) when x G K and the empty set when x is not ...
... solution is naturally lacking: Let W be a function from X x Y to R. We consider the family of minimization problems ... solutions to our minimization problem. One of the main issues of optimization theory is to study the set-valued map G ...