In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers. Let and let be a given function having a third derivative on the range , and such that
for all . Suppose for and . Then
The Ky Fan inequality is the special case of Levinson's inequality where
- Scott Lawrence and Daniel Segalman: A generalization of two inequalities involving means, Proceedings of the American Mathematical Society. Vol 35 No. 1, September 1972.
- Norman Levinson: Generalization of an inequality of Ky Fan, Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134.