Inegalitate usurica
Posted: Thu Apr 30, 2009 9:11 pm
\( \left|\begin{array}{c}
a_{1},\ a_{2},\dots,\ a_{n}\in\mathbb{R},\ \lambda\in\left(0,\ \infty\right),\ n\in\mathbb{N},\ n\ge2\\
a_{1}^{2}+a_{2}^{2}+\dots+a_{n}^{2}\le\lambda^{2}\end{array}\right|\Longrightarrow a_{1}^{3}+a_{2}^{3}+\dots+a_{n}^{3}\le\lambda^{3}. \)
a_{1},\ a_{2},\dots,\ a_{n}\in\mathbb{R},\ \lambda\in\left(0,\ \infty\right),\ n\in\mathbb{N},\ n\ge2\\
a_{1}^{2}+a_{2}^{2}+\dots+a_{n}^{2}\le\lambda^{2}\end{array}\right|\Longrightarrow a_{1}^{3}+a_{2}^{3}+\dots+a_{n}^{3}\le\lambda^{3}. \)