Characterization of intermediate values of the triangle inequality II

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. Cn that satisfy 0 ≤ Cn ≤ Σj=1n ‖xj‖ − ‖Σj=1nxj‖, x1,...,xn ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.