ThmDex – An index of mathematical definitions, results, and conjectures.
Complex binomial inequality
Formulation 0
Let $z_1, \ldots, z_N \in \mathbb{C}$ each be a D1207: Complex number.
Let $p \in (0, \infty)$ be a D5407: Positive real number.
Then \begin{equation} \sum_{n = 1}^N |z_n| \leq N \left( \sum_{n = 1}^N |z_n|^p \right)^{1 / p} \end{equation}
Proofs
Proof 0
Let $z_1, \ldots, z_N \in \mathbb{C}$ each be a D1207: Complex number.
Let $p \in (0, \infty)$ be a D5407: Positive real number.
This result is a particular case of R4727: Euclidean real binomial inequality. $\square$