## 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 86

Contents Introduction 1 1 Continuity of Set- Valued Maps 15 1.1 Limits of Sets 16 1.1.1 Definitions 16 1.1.2 The Compactness

**Theorem**23 1.1.3 The Duality

**Theorem**24 1.1.4 Convex Hull of Limits 26 1.2 Calculus of Limits 27 1.2.1 Direct ...

3 Existence and Stability of an Equilibrium 77 3.1 Ky Fan's Inequality 80 3.2 Equilibrium and Fixed Point

**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 ...

... The Viability

**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**...

Indeed, the two basic

**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 ...

Nonlinear Functional Analysis We are convinced that many problems can be regarded as inclusions given F : X ~> Y and y eY, find x G X such that F(x) 3 y Most

**theorems**on existence of solutions to nonlinear equations can be extended to ...

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