Mahler's inequality
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:
when xk, yk > 0 for all k.
Proof
By the inequality of arithmetic and geometric means, we have:
and
Hence,
Clearing denominators then gives the desired result.
See also
References
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