THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES
2018 ◽
Vol 99
(1)
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pp. 130-136
Keyword(s):
We study the classical Rosenthal–Szasz inequality for a plane whose geometry is determined by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case where the unit circle of the norm is given by a Radon curve, we obtain an inequality which is completely analogous to the Euclidean case. For arbitrary norms we obtain an upper bound for the perimeter calculated in the anti-norm, yielding an analogous characterisation of all curves of constant width. To derive these results, we use methods from the differential geometry of curves in normed planes.
2017 ◽
Vol 69
(4)
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pp. 1475-1484
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2013 ◽
Vol 55
(1)
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pp. 201-206
2006 ◽
Vol 153
(11)
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pp. 1699-1704
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2006 ◽
Vol 204
(1)
◽
pp. 241-261
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2014 ◽
Vol 18
(4)
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pp. 1283-1291
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2009 ◽
Vol 52
(3)
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pp. 342-348
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2018 ◽
Vol 23
(6)
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pp. 461-464
2015 ◽
Vol 196
◽
pp. 347-361
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