## The computation of fixed points and applications |

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### Contents

Notation vj Chapter I Brouwers Theorem l | 1 |

Some Applications of Brouwers Theorem | 17 |

Triangulations | 24 |

Copyright | |

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### Common terms and phrases

affine combination affine hull affinely independent approximate fixed point approximation to F artificial labels barycentric subdivision Brouwer's theorem Chapter closed n-cell compact completely-labelled simplices computation continuous function contradiction convex convex hull convex set coordinate denote dimension directional density Eaves example F is u.s.c. F with respect facets of type follows function f grid hence homeomorphism homotopy integer labelling Jacobian K-K-M lemma Kakutani's l.l Definition Let F Let G lies linear programming Mathematical matrix Merrill's algorithm mesh G n-l)-simplex n-simplices node of F nonempty Nonlinear Complementarity Problem Nonlinear Programming Note number of simplices obtain p.l. approximation path permutation piecewise linear point of f primitive sets Programming Proof prove result Saigal satisfying Scarf Section Seiten simplex simplices of G solution Sperner's lemma Step tion triangulation G triangulation with crogs u.s.c. mapping unique vector labelling vertex vertices carry y,ir zero