## Title data

Baier, Robert:

**Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.**

*In:* Staicu, Vasile
(ed.):
Differential Equations, Chaos and Variational Problems. -
Basel
: Birkhäuser
,
2007
. - pp. 49-60
. - (Progress in Nonlinear Differential Equations and Their Applications
; 75
)

ISBN 978-3-7643-8481-4

DOI: https://doi.org/10.1007/978-3-7643-8482-1_4

Review: |

## Abstract in another language

Generalized Steiner points and the corresponding selections for set-valued maps share interesting commutation properties with set operations which make them suitable for the set-valued numerical problems presented here. This short overview will present first applications of these selections to standard problems in this area, namely representation of convex, compact sets in |Rn and set operations, set-valued integration and interpolation as well as the calculation of attainable sets of linear differential inclusions. Hereby, the convergence results are given uniformly for a dense countable representation of generalized Steiner points/selections. To achieve this aim, stronger conditions on the set-valued map F have to be taken into account, e.g. the Lipschitz condition on F has to be satisfied for the Demyanov distance instead of the Hausdorff distance. To establish an overview on several applications, not the strongest available results are formulated in this article.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Additional notes: | Contents:
1. Preliminaries 2. Representation and Arithmetics of Sets 3. Regularity of Set-Valued Maps 4. Set-Valued Interpolation and Quadrature Methods 5. Linear Differential Inclusions 6. Conclusions |

Keywords: | Generalized Steiner selections; Set-valued quadrature methods and interpolation; Linear differential inclusions; Attainable sets; Lipschitz and absolutely continuous selections; Set operation |

Subject classification: | Mathematics Subject Classification Code: 54C65 (93B03 93C05 28B20) |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 04 Mar 2021 09:47 |

Last Modified: | 25 Mar 2021 06:04 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63666 |