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."
Results 1-5 of 40
These include: • Limits and Continuity • Linear Functional Analysis • Nonlinear Functional Analysis (existence and approximation of solutions to equations and inclusions) • Tangents and Normals • Differentiation of Maps • Gradients of ...
236 6.2.2 Other Convex Epiderivatives 240 6.3 Epidifferential Calculus 242 6.4 Generalized Gradient 248 6.4.1 Subdifferentials and Generalized Gradients . . 248 6.4.2 Limits of Subdifferentials and Gradients .
... Conjugate Functions of Epilimits 289 7.6 Graphical Convergence of Gradients 294 7.6.1 Convergence of Gradients of Smooth Functions 295 7.6.2 Convergence of Subdifferentials of Convex Functions 297 7.7 Asymptotic Epiderivatives 300 8 ...
The crucial revolution in the history of the concept of gradients happened in the sixties when J.- J. Moreau and R. T. Rock- afellar proposed in the framework of convex analysis the notion of subdifferential of a convex function, ...
Gradients of Functions and the Fermat Rule The particular case of real-valued functions deserves a study by itself for taking into account the order relation of real numbers. We are led to do so whenever we look for a minimizer of a ...