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 79
... Open Mapping and Closed Graph Theorems 57 2.3 Uniform Boundedness Theorem 61 2.4 The Bipolar Theorem 62 2.5 Transposition of Closed Convex Process 67 2.6 Upper Hemicontinuous Maps 74 3 Existence and Stability of an Equilibrium 77 3.1 Ky.
... Theorems 83 3.2.1 The Equilibrium Theorem 83 3.2.2 Fixed Point Theorems 86 3.2.3 The Leray-Schauder Theorem 89 3.3 Ekeland's Variational Principle 91 3.4 Constrained Inverse Function Theorem 93 3.4.1 Derivatives of Single- Valued Maps ...
... Theorem 387 10.1.1 Solutions to Differential Inclusions 388 10.1.2 Statements of the Viability Theorems 389 10.1.3 Viability Kernels 392 10.1.4 Viability and Equilibria 393 10.2 Applications of the Viability Theorem 394 10.2.1 Linear ...
... theorems on continuous linear operators due to Banach, the Closed Graph Theorem (equivalent to the Open Mapping Principle) and the Banach- Steinhaus Theorem, can be adapted to closed convex processes. The first one states that a closed ...
... Theorem. We shall prove an equivalent statement, called the Equilibrium Theorem, which provides the existence of an equilibrium of a set-valued map, a solution to the inclusion F(x) 3 0. Of course, for applications, we need not only to ...