Characterization of a generalized triangle inequality in normed spaces

2011/09/08 by F. Dadipour, M. S. Moslehian, J. M. Rassias +1 · 1 citation
Mathematics · #math.FA #math.CA #msc:46C15 #msc:46B20 #msc:46C05

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published as Nonlinear Anal-TMA 75 (2012), no. 2, 735-741 · 11 Pages, to appear in Nonlinear Anal-TMA

arxiv created 2011/09/08 · arxiv updated 2012/03/21

Abstract

For a normed linear space (X,|⋅|) and p>0 we characterize all n-tuples (μ₁,...,μ_n)∈ℝⁿ for which the generalized triangle inequality of the second type ‖x₁+...+x_n‖^p≤(|x₁|^p)/(μ₁)+...+(|x_n|^p)/(μ_n) holds for any x₁,...,x_n∈ X. We also characterize (μ₁,...,μ_n)∈ℝⁿ for which the reverse of the inequality above holds.

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