## KKM Theory and Applications in Nonlinear AnalysisThis reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis. |

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### Contents

Introduction | 1 |

Mappings | 22 |

The KKM Theory and Related Topics | 37 |

Topological Intersection and Minimax Inequality Theory | 199 |

Abstract Economic Models and Generalized Games | 229 |

Variational Inequalities Part I | 325 |

Variational Inequalities Part II | 381 |

Spaces | 430 |

Applications to MultiObjective Optimization | 463 |

Applications to Game Theory | 519 |

Applications to Mathematical Economics | 545 |

References | 575 |

Index | 613 |

### Common terms and phrases

Ai(x application of Theorem asymptotic plane Banach space Browder-Fan fixed point closed and convex closed convex compact and convex compact convex subset compactly open complementarity problem concave convex set convex topological vector convex values Corollary corresponding define Definition denote equilibria equilibrium point essential relative existence theorems exists a non-empty exists a point Fan minimax inequality Fan's finite dimensional finite intersection property fixed point theorem following conditions following result function Hausdorff topological vector Hence hyperconvex metric space hypotheses of Theorem Ky Fan minimax Lemma locally convex spaces locally convex topological lower semicontinuous mapping F mapping with non-empty Math maximal elements minimax theorems non-compact non-empty closed non-empty compact convex non-empty compact subset non-empty convex subset non-empty subset Note open neighborhood paracompact quasi-concave quasi-variational inequalities Re(u resp saddle point semicontinuous with non-empty sequence Suppose Tarafdar topological space topological vector space upper semicontinuous variational inequalities weakly