Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841216 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 7 Pages |
Abstract
For a normed linear space (X,‖⋅‖)(X,‖⋅‖) and p>0p>0 we characterize all nn-tuples (μ1,…,μn)∈Rn(μ1,…,μn)∈Rn for which the generalized triangle inequality of the second type ‖x1+⋯+xn‖p≤‖x1‖pμ1+⋯+‖xn‖pμn holds for any x1,…,xn∈Xx1,…,xn∈X. We also characterize (μ1,…,μn)∈Rn(μ1,…,μn)∈Rn for which the reverse of the inequality above holds.
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Authors
Farzad Dadipour, Mohammad Sal Moslehian, John M. Rassias, Sin-Ei Takahasi,