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Preface

0.Preliminaries

1.Multivalued maps

1.1Some examples

1.2Continuity of multivalued maps

1.2.1Small and complete preimages of a set

1.2.2Upper and lover semicontinuity, continuity, closedness of multimaps

1.2.3Multivalued maps into a metric space

1.3Operations on multivalued maps

1.3.1Set-theoretic operations

1.3.2Algebraic and other operations

1.3.3Theorem of maximum

1.4Continuous selections and approximations of multivalued maps

1.5Measurable multivalued functions and the superposition multioperator

1.5.1Measurable multifunctions and a multivalued integral

1.5.2The Carathéodory conditions and the Filippov implicit function lemma

1.5.3The superposition multioperator

2.Fixed points and topological degree

2.1Fixed points of contractive multimaps

2.1.1The Nadler theorem

2.1.2Contractive multimaps depending on a parameter

2.1.3Equations with surjective linear operators

2.1.4Inequalities of Caristi type and α-contractive multimaps

2.1.5Fixed points of weakly α-contractive multimaps

2.2Topological degree of compact multivalued vector fields

2.3Topological degree of condensing multivalued vector fields

2.4Some properties of the fixed point set

2.5The Browder–Ky Fan fixed point theorem and variational inequalities

3.Differential inclusions and control systems

3.1Differential inclusions. Some examples

3.2Existence theorems and properties of the solution sets

3.3Periodic solutions of differential inclusions

3.4Control systems

4.On some applications

4.1Generalized dynamical systems

4.1.1General properties

4.1.2Rest points of one-sided dynamical systems

4.2On applications in theory of games and mathematical economics

4.2.1Optimal strategies in zero-sum games

4.2.2An equilibrium in a model of a competitive economics

Bibliographical comments and additions

Bibliography

Index