Talenti–Tura´n

Talenti’s Inequality If a > 0 and f is positive and decreasing on [a, b] then

log

( 1 +

1 + af(a)

f

) ≤ ∫ b a

f(t)

1 + tf(t) dt.

Comment This result has been extended and provided with an inverse by Lemmert & Alzer.