### 抜粋

We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods. We already derived such a theorem in [11], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.

元の言語 | 英語 |
---|---|

ページ（範囲） | 1190-1204 |

ページ数 | 15 |

ジャーナル | Numerical Functional Analysis and Optimization |

巻 | 32 |

発行部数 | 11 |

DOI | |

出版物ステータス | 出版済み - 12 1 2011 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Analysis
- Control and Optimization
- Signal Processing
- Computer Science Applications

### これを引用

*Numerical Functional Analysis and Optimization*,

*32*(11), 1190-1204. https://doi.org/10.1080/01630563.2011.594348