Sea $ 0 < x_{1}\leq\frac {x_{2}}{2}\leq\cdots\leq\frac {x_{n}}{n}, 0 < y_{n}\leq y_{n - 1}\leq\cdots\leq y_{1},$ Demuestre que $ (\sum_{k = 1}^{n}x_{k}y_{k})^2\leq(\sum_{k = 1}^{n}y_{k})(\sum_{k = 1}^{n}(x_{k}^2 - \frac {1}{4}x_{k}x_{k - 1})y_{k}).$ donde $ x_{0} = 0.$