MathDB

Let

a_1,a_2,\ldots ,a_n

n

real numbers such that

0<a\le a_k\le b

for

k=1,2,\ldots ,n

. If

m_1=\frac{1}{n}(a_1+a_2+\cdots+a_n)

and

m_2=\frac{1}{n}(a_1^2+a_2^2+\cdots + a_n^2)

, prove that

m_2\le\frac{(a+b)^2}{4ab}m_1^2

and find a necessary and sufficient condition for equality.

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