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Characterization of intermediate values of the triangle inequality. II. (English) Zbl 1310.46020

Summary: In [K. Mineno et al., Math. Inequal. Appl. 15, No. 4, 1019–1035 (2012; Zbl 1263.46025)], a norm inequality was established which characterizes all intermediate values of the triangle inequality, i.e., \(C_n\) that satisfies \(0\leq C_n\leq\sum_{j=1}^n\|x_j\|-\|\sum_{j=1}^nx_j\|\), \(x_1,\dots,x_n\in X\). Here we study when this norm inequality attains equality in strictly convex Banach spaces.

MSC:

46B20 Geometry and structure of normed linear spaces
26D20 Other analytical inequalities

Citations:

Zbl 1263.46025
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Full Text: DOI

References:

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