Prove that if \(a, x\), and \(y\) are positive real numbers then\[2 \max \{x, y\} \delta\{2 \max \{x, y\} ;(a, \infty)\} \leq 2 x \delta\left\{x ;\left(\frac{1}{2}a, \inftyight)ight\}+2 y \delta\left\{y ;\left(\frac{1}{2} a, \inftyight)ight\}\]