In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.
@article{bwmeta1.element.doi-10_2478_s11533-013-0369-7,
author = {Hiroki Sano and Tamotsu Izumida and Ken-Ichi Mitani and Tomoyoshi Ohwada and Kichi-Suke Saito},
title = {Characterization of intermediate values of the triangle inequality II},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {778-786},
zbl = {1310.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0369-7}
}
Hiroki Sano; Tamotsu Izumida; Ken-Ichi Mitani; Tomoyoshi Ohwada; Kichi-Suke Saito. Characterization of intermediate values of the triangle inequality II. Open Mathematics, Tome 12 (2014) pp. 778-786. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0369-7/
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