In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers. Let
a>0
f
(0,2a)
f'''(x)\geq0
for all
x\in(0,2a)
0<xi\leqa
0<pi
i=1,\ldots,n
| -f\left( | ||||||||||
|
| \right)\le | ||||||||||
|
| -f\left( | ||||||||||
|
| ||||||||||
|
\right).
The Ky Fan inequality is the special case of Levinson's inequality, where
pi=1, a=
1 | |
2 |
,andf(x)=logx.
Generalization of an inequality of Ky Fan, Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134.