On a nonlinear $p$-inequality

13 Aug 2018  ·  Abdelhakim Ahmed A. ·

We obtain the necessary and sufficient conditions on real sequences $(\beta_{i})$ for the satisfaction of the generalized triangle inequality \begin{equation} \|\sum_{i\geq 1} v_{i}\|^{p} \leq \sum_{i\geq 1}{{\beta_{i}} \| v_{i}\|^{p}}.\tag{I} \end{equation} Sequences $(\beta_{i})$ for which the reverse of the inequality (I) holds are characterized as well...

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Functional Analysis