Characterization of intermediate values of the triangle inequality II

Hiroki Sano; Tamotsu Izumida; Ken-Ichi Mitani; Tomoyoshi Ohwada; Kichi-Suke Saito

Open Mathematics (2014)

  • Volume: 12, Issue: 5, page 778-786
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Hiroki Sano, et al. "Characterization of intermediate values of the triangle inequality II." Open Mathematics 12.5 (2014): 778-786. <http://eudml.org/doc/269713>.

@article{HirokiSano2014,
abstract = {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.},
author = {Hiroki Sano, Tamotsu Izumida, Ken-Ichi Mitani, Tomoyoshi Ohwada, Kichi-Suke Saito},
journal = {Open Mathematics},
keywords = {Triangle inequalities; Strictly convex Banach spaces; Norm inequality; triangle inequalities; strictly convex Banach spaces; norm inequality},
language = {eng},
number = {5},
pages = {778-786},
title = {Characterization of intermediate values of the triangle inequality II},
url = {http://eudml.org/doc/269713},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Hiroki Sano
AU - Tamotsu Izumida
AU - Ken-Ichi Mitani
AU - Tomoyoshi Ohwada
AU - Kichi-Suke Saito
TI - Characterization of intermediate values of the triangle inequality II
JO - Open Mathematics
PY - 2014
VL - 12
IS - 5
SP - 778
EP - 786
AB - 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.
LA - eng
KW - Triangle inequalities; Strictly convex Banach spaces; Norm inequality; triangle inequalities; strictly convex Banach spaces; norm inequality
UR - http://eudml.org/doc/269713
ER -

References

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