Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 49: Issue 1
Reverse triangle inequality. Antinorms and semi-antinorms
Authors: Maria Moszyńska 1 and Wolf-Dieter Richter 2
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  • 1 University of Warsaw Institute of Mathematics Banacha 2 02-097 Warszawa Poland
  • 2 University of Rostock Institute of Mathematics Ulmenstrasse 69, Haus 3 D-18057 Rostock Germany
DOI:
https://doi.org/10.1556/sscmath.49.2012.1.1192
Page Count:
120–138
Publication Date:
01 Mar 2012
Online Publication Date:
03 Mar 2012
Article Category:
Research Article

Article Info

Page Count:
120–138
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The paper concerns a biunique correspondence between some positively homogeneous functions on ℝn and some star-shaped sets with nonempty interior, symmetric with respect to the origin (Theorems 3.5 and 4.3).

  • Ansari, A. H. and Moslehian, M. S., Refinements of reverse triangle inequalities in inner product spaces, J. Inequalities in Pure and Applied Math., 6(3), Article 64 (2005). MR 2164305

  • Beckenbach, E. F. and Bellmann, R., Inequalities, Springer Verlag, 1965. MR 33#236

  • Diaz, J. B. and Metcalf, F. T., A complementary triangle inequality in Hilbert and Banach Spaces, Proc. AMS, 17(1) (1966), 88–97. MR 32#6184

    Metcalf F. T. , 'A complementary triangle inequality in Hilbert and Banach Spaces ' (1966 ) 17 Proc. AMS : 88 -97.

    • Search Google Scholar

  • Dragomir, S. S., Reverses of the triangle inequality in Banach Spaces, J. Inequalities in Pure and Applied Math., 6(5), Article 129 (2005). MR 2006g:46036

  • Ewald, G., Combinatorial Convexity and Algebraic Geometry, Springer Verlag, 1996. MR 97i:52012

  • Gardner, R. J., Geometric Tomography, Cambridge University Press, 1995. MR 96j:52006

  • Hansen, G. and Martini, H., Starshapedness vs. convexity, Results Math., 59 (2011), 185–197.

    Martini H. , 'Starshapedness vs. convexity ' (2011 ) 59 Results Math. : 185 -197.

  • Martini, H. and Wencel, W., An analogue of the Krein-Milman theorem for starshaped sets, Beitr. Algebra Geom., 44 (2003), 441–449.

    Wencel W. , 'An analogue of the Krein-Milman theorem for starshaped sets ' (2003 ) 44 Beitr. Algebra Geom. : 441 -449.

    • Search Google Scholar

  • Martini, H. and Swanepoel, K. J., Antinorms and Radon curves, Aequationes Math., 72 (2006), 110–138. MR 2007f:52001

    Swanepoel K. J. , 'Antinorms and Radon curves ' (2006 ) 72 Aequationes Math. : 110 -138.

  • Moszyńska, M., Selected Topics in Convex Geometry, Birkhäuser Verlag, 2006. MR 2006g:52001

  • Nakai, M. and Tada, T., The reverse triangle inequality in normed spaces, New Zeeland J. Math., 25(2) (1996), 181–193. MR 97m:46024

    Tada T. , 'The reverse triangle inequality in normed spaces ' (1996 ) 25 New Zeeland J. Math. : 181 -193.

    • Search Google Scholar

  • Richter, W.-D., On l 2;p-circle numbers, Lithuanian Math. J., 48(2) (2008), 228–234. MR 2009e:28020

    Richter W.-D. , 'On l2;p-circle numbers ' (2008 ) 48 Lithuanian Math. J. : 228 -234.

  • Richter, W.-D., On the π-function for non-convex l 2;p-circles discs, Lithuanian Math. J., 48(3) (2008), 332–338. MR 2010a:52012

    Richter W.-D. , 'On the π-function for non-convex l2;p-circles discs ' (2008 ) 48 Lithuanian Math. J. : 332 -338.

    • Search Google Scholar

  • Rockafellar, R. T., Convex Analysis, Princeton University Press, 1970. MR 43#445

  • Schneider, R., Convex Bodies: the Brunn-Minkowski Theory, Cambridge University Press, 1993. MR 94d:52007

  • Thompson, A. C., Minkowski Geometry, Cambridge University Press, 1996. MR 97f:52001

  • Yosida, K., Functional Analysis, Springer Verlag, 1965. MR 31#5054
Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896
Keywords:
Primary 26D07, 52A21, 52A99, 52B11, 46N30, 26B99; positively homogeneous function; norm; semi-norm; semiantinorm; Minkowski functional; star body; radial function

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