@article{3064601,
    title = "Characterization of a generalized triangle inequality in normed spaces",
    author = "Dadipour, F. and Moslehian, M.S. and Rassias, J.M. and Takahasi, S.-E.",
    journal = "Nonlinear Analysis, Theory, Methods and Applications",
    year = "2012",
    volume = "75",
    number = "2",
    pages = "735-741",
    doi = "10.1016/j.na.2011.09.004",
    keywords = "N-tuples;  Norm inequality;  Normed linear space;  Normed spaces;  Triangle inequality, Banach spaces",
    abstract = "For a normed linear space (X,∥ · ∥) and p>0 we characterize all n-tuples (μ1,⋯,μn) ∈ℝn for which the generalized triangle inequality of the second type ∥ x1+⋯+ xn∥p≤ ∥ x1∥p/μ1+⋯+∥ x n∥p/μn holds for any X 1,⋯,Xn∈X. We also characterize (μ1,⋯,μn)∈ℝn for which the reverse of the inequality above holds. © 2011 Elsevier Ltd. All rights reserved."
}