## Topological Methods in Nonlinear Functional Analysis, Volumes 1-2This volume contains the proceedings of the special session on Fixed Point Theory and Applications held during the Summer Meeting of the American Mathematical Society at the University of Toronto, August 21-26, 1982. The theory of contractors and contractor directions is developed and used to obtain the existence theory under rather weak conditions. Theorems on the existence of fixed points of nonexpansive mappings and the convergence of the sequence of iterates of nonexpansive and quasi-nonexpansive mappings are given. Degree of mapping and its generalizations are given in detail. A class of eventually condensing mappings is studied and multivalued condensing mappings with multiple fixed points are also given. Topological fixed points, including the study of the Nielsen number of a selfmap on a compact surface, extensions of a well-known result of Krasnoselskii's Compression of a Cone Theorem, are given. Also, fixed points, antipodal points, and coincidences of multifunctions are discussed. Several results with applications in the field of partial differential equations are given. Application of fixed point theory in the area of Approximation Theory is also illustrated. |

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### Contents

1 | |

The Degree of Mapping and its Generalizations | 15 |

Multiple Fixed Points of Compact Maps on Wedgelike ANRS in Banach Spaces | 41 |

The Nielsen Numbers on Surfaces | 59 |

A Good Class of Eventually Condensing Maps | 99 |

Iteration Process for Nonexpansive Mappings | 115 |

The Best Approximation of Bivariate Functions by Separable Functions | 125 |

Positive Solutions of Operator Equations in the Nondifferentiable Case | 137 |

Fixed Points and Sequences of Iterates in Locally Convex Spaces | 159 |

Fixed Point Theorems and Jung Constant in Banach Spaces | 167 |

Some Results on Multiple Positive Fixed Points of Multivalued Condensing Maps | 171 |

Some Problems and Results in Fixed Point Theory | 179 |

Contractive Definitions Revisited | 189 |

Fixed Points Antipodal Points and Coincidences of nAcyclic Multifunctions | 207 |

A Coincidence Theorem for Topological Vector Spaces | 213 |

Some Random Fixed Point Theorems | 215 |

On Fixed Points of Nonexpansive Mappings | 147 |

Large Oscillations of Forced Nonlinear Differential Equations | 151 |

### Other editions - View all

Topological Methods in Nonlinear Functional Analysis: Proceedings of the ... S. P. Singh,. summer meeting No preview available - 1983 |

Topological Methods in Nonlinear Functional Analysis, Volumes 1-2 Sankatha Prasad Singh,S. Thomeier,B. Watson No preview available - 1983 |

### Common terms and phrases

1983 American Mathematical acyclic approximation assume asymptotically bounded sets bounded subset class of maps classical degree common fixed point compact map compact metric space condensing mappings condition Contemporary Mathematics Volume continuous map continuous selfmap contraction mappings contractive definition contractor directions converges strongly converges weakly convex set convex subset Corollary d(Sx d(Tx defined degree function degree theory denote exists finite fixed point free fixed point index fixed point theorem Fréchet differentiable Hence Hilbert space homeomorphism implies iterative Lemma Leray–Schauder Let F linear locally convex spaces map f Math Mathematics Volume 21 method metric space X,d monotone multivalued map nonempty nonexpansive mappings norm open set open subset ordered Banach space positive upper problem Proof of Theorem Proposition pseudo-monotone reflexive Banach space Reich satisfying sequence solutions Splitting Lemma subspace Suppose topological wedgelike