ABSTRACT
Opial’s Inequalities (a) If f is absolutely continuous on [0, h] with f(0) = 0 then ∫ h
|ff ′| ≤ h 2
f ′2, (1)
with equality if and only if f(x) = cx. The constant is best possible. (b) If a is a non-negative (2n+ 1)-tuple satisfying
a2k ≤ min{a2k−1, a2k+1}, 1 ≤ k ≤ n, and if a0 = 0 then (
(∆a2k)
)2 ≥
(−1)k+1ak.
