## Fixed Point Theory and ApplicationsThis book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type. |

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### Contents

12 | |

3 Continuation Methods for Contractive and Nonexpansive Mappings | 19 |

4 The Theorems of Brouwe Schauder and Mönch | 28 |

5 Nonlinear Alternatives of LeraySchauder Type | 48 |

6 Continuation Principles for Condensing Maps | 65 |

7 Fixed Point Theorems in Conical Shells | 78 |

8 Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces | 94 |

### Other editions - View all

Fixed Point Theory and Applications Ravi P. Agarwal,Maria Meehan,Donal O'Regan No preview available - 2009 |

Fixed Point Theory and Applications Ravi P. Agarwal,Maria Meehan,Donal O'Regan No preview available - 2001 |

### Common terms and phrases

addition Amer Anal apply Theorem assume Banach space boundary bounded bounded subset called chapter choose closed compact map complete condensing map Consequently Consider constant continuous map contractive contractive maps contradicts converges convex linear topological convex subset deﬁned Deﬁnition denote easy equations essential establish Exercise exists a continuous extension fact ﬁnite ﬁrst ﬁxed point fixed point theorem following conditions function given guarantees Hausdorff hold immediately implies inessential integral least Let E linear topological space locally convex linear map F Math metric space multivalued mappings nonempty nonexpansive map normed linear space Notice O’Regan open subset operator particular present principle problem Proof Proof Let prove Remark result satisﬁes Schauder sequence Show that F solution Suppose that F true unique upper values vector