Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"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."
"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."
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This is not always the solution, for, by so doing, many important structural properties may be unfortunately lost; others are useless artifacts, making life more difficult rather than more simple. These points of view, which were widely ...
... Monotone Maps 106 3.5.3 Yosida Approximations Ill 3.6 Eigenvectors of 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 .
222 6.1.2 Contingent Epiderivatives 224 6.1.3 Fermat and Ekeland Rules 232 6.1.4 Elementary Properties 234 6.2 Other Epiderivatives 236 6.2.1 Adjacent and Circatangent Epiderivatives . . . 236 6.2.2 Other Convex Epiderivatives 240 6.3 ...
270 7.2 Convergence Theorems 270 7.3 Epilimits 274 7.3.1 Definitions and Elementary Properties 274 7.3.2 Convergence of Infima and Minimizers 281 7.3.3 Variational Systems 284 7.4 Epilimits of Sums and Composition Products 286 7.5 ...
5 Properties of Normal Cones In Finite Dimensional Vector Spaces 158 4.6 Properties of m^-order Contingent Sets 172 4.7 Properties of mt/l-order Adjacent Sets 174 Introduction It is a fact that in mathematical sciences there xix.