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Some remarks on the triangle inequality for norms. (English) Zbl 1147.46020

Summary: Remarks about strengthening of the triangle inequality and its reverse inequality in normed spaces for two and more elements are collected. There is also a discussion of the Foscjr-Muszely equality for \(n\)-elements in a normed space. Some other estimates which follow from the triangle inequality are also presented.

MSC:

46B99 Normed linear spaces and Banach spaces; Banach lattices
51M16 Inequalities and extremum problems in real or complex geometry
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