Levinson's inequality

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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.