# Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment

Agnieszka Bogdewicz; Jerzy Grzybowski

Banach Center Publications (2009)

- Volume: 84, Issue: 1, page 75-88
- ISSN: 0137-6934

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topAgnieszka Bogdewicz, and Jerzy Grzybowski. "Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment." Banach Center Publications 84.1 (2009): 75-88. <http://eudml.org/doc/281750>.

@article{AgnieszkaBogdewicz2009,

abstract = {Let $(ℝ,||·||_)$ be a Minkowski space with a unit ball and let $ϱ_H^\{\}$ be the Hausdorff metric induced by $||·||_\{\}$ in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to $ϱ_H^\{Bⁿ\}$ for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace $(²,ϱ_H^\{\})$ over any two-dimensional Minkowski space.},

author = {Agnieszka Bogdewicz, Jerzy Grzybowski},

journal = {Banach Center Publications},

keywords = {convex body; Minkowski space; metric midpoint; metric segment},

language = {eng},

number = {1},

pages = {75-88},

title = {Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment},

url = {http://eudml.org/doc/281750},

volume = {84},

year = {2009},

}

TY - JOUR

AU - Agnieszka Bogdewicz

AU - Jerzy Grzybowski

TI - Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment

JO - Banach Center Publications

PY - 2009

VL - 84

IS - 1

SP - 75

EP - 88

AB - Let $(ℝ,||·||_)$ be a Minkowski space with a unit ball and let $ϱ_H^{}$ be the Hausdorff metric induced by $||·||_{}$ in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to $ϱ_H^{Bⁿ}$ for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace $(²,ϱ_H^{})$ over any two-dimensional Minkowski space.

LA - eng

KW - convex body; Minkowski space; metric midpoint; metric segment

UR - http://eudml.org/doc/281750

ER -

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