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 83
... Set- Valued Maps 179 5.1 Contingent Derivatives 181 5.2 Adjacent and Circatangent Derivatives 189 5.2.1 Definitions ... Set- Valued Map Theorem 203 5.4.1 Stability and Approximation of Inclusions . . . 203 5.4.2 Localization of Inverse ...
... Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and Maximal Monotone Maps . 104 4.1 Contingent Cone at a Boundary Point may be the Whole Space 122 ...
... set-valued maps. Despite the emergence of exciting new vistas for the applications of mathematics, our long familiarity with sequences (of elements) and with (single-valued) ... map is bijective when we want to solve an equation. Indeed, the ...
... set- valued maps and inclusions. They also arise when we wish to treat a problem qualitatively, by looking for solutions common to a set ... map associating with x the point f(x) when x G K and the empty set when x is not in K. 4. Unilateral ...
... set-valued map G (nonvacuity, continuity and differentiability in a suitable sense, and so on.) We shall call G the marginal map. It is no wonder that game theory and mathematical economics use set- valued maps in a natural way. 7 ...