Mahler's inequality

Last updated

In mathematics, Mahler's inequality, named after Kurt Mahler, states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means:

Contents

when for all .

Proof

By the inequality of arithmetic and geometric means, we have:

and

Hence,

Clearing denominators then gives the desired result.

See also

References