Set-Valued Analysis

ISBN-13: 9780817648473 / Angielski / Miękka / 2008 / 484 str.

Jean-Pierre Aubin; Ha(c)La]ne Frankowska

Opis

"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"

Recenzje

From the reviews:

"An elegantly written, introductory overview of the field, with a near-perfect choice of what to include and what not, enlivened by historical tidbits and made eminently readable throughout by a 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 non-intimidating even to a beginning graduate student." -Journal of the Indian Institute of Science

"Highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." -Mathematical Reviews

"A valuable resource for workers in many fields...contains a lot of information and many interesting asides....goes a long way toward providing a much needed basic resource on the subject." -Bulletin of the AMS

"Provides a thorough introduction to the multivalued or set-valued analysis, gathering both old and new results in an up-to-date perspective. ...Graduate students and mathematicians of every persuasion will welcome this unparallel guide to set-valued analysis." -Zentralblatt Math

"The book gives an in-depth introduction and overview of the field. ... the book is a basic resource for graduate students and researchers who are interested in the mathematics required to apply set-valued analysis in their work." (IEEE Control Systems Magazine, Vol. 30, April, 2010)

Spis treści

Introduction.- Continuity of Set-Valued Maps.- Closed Convex Processes.- Existence and Stability of an Equilibrium.- Tangent Cones.- Derivatives of Set-Valued Maps.- Epiderivatives of Extended Functions.- Graphical & Epigraphical Convergence.- Measurability and Integration of Set-Valued Maps.- Selections and Parametrization.- Differential Inclusions.- Bibliographical Comments.- Bibliography.- Index.