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. MR33#236
Diaz, J. B. and Metcalf, F. T., A complementary triangle inequality in Hilbert and Banach Spaces, Proc. AMS, 17(1) (1966), 88–97. MR32#6184
Metcalf F. T., 'A complementary triangle inequality in Hilbert and Banach Spaces' (1966) 17Proc. AMS: 88-97.
Metcalf F. T.A complementary triangle inequality in Hilbert and Banach SpacesProc. AMS1966178897)| false