Mandal, Kalidas and Sain, Debmalya and Paul, Kallol
(2019)
*A Geometric Characterization of Polygonal Radon Planes.*
In: JOURNAL OF CONVEX ANALYSIS, 26
(4).
pp. 1113-1123.

## Abstract

We study unit circles of polygonal Radon planes from a geometric point of view. In particular, we prove that a two-dimensional real polygonal Banach space X cannot be a Radon plane if the number of vertices of its unit circle is 4n, for some n is an element of N. Also we obtain a complete characterization of polygonal Radon planes in terms of a tractable geometric concept introduced in this article. It follows from our characterization that every regular polygon with 4n+2 vertices, where n is an element of N, is the unit circle of a Radon plane. Furthermore, we describe types of Radon planes for which the unit circles are hexagons, but not regular ones.

Item Type: | Journal Article |
---|---|

Additional Information: | copyright for this article belongs to HELDERMANN VERLAG |

Keywords: | Radon plane; Birkhoff-James orthogonality; polygonal Banach space |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Id for Latest eprints |

Date Deposited: | 29 Nov 2019 10:25 |

Last Modified: | 29 Nov 2019 10:25 |

URI: | http://eprints.iisc.ac.in/id/eprint/64024 |

### Actions (login required)

View Item |