Mahler's inequality [SEP] named after
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 "x", "y"  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
Littlewood maximal inequality
- Inequality of arithmetic and geometric means
- Ky Fan inequality
- Levinson's inequality
- Maclaurin's inequality
- Mahler's inequality
- Muirhead's inequality
- Newton's inequalities
- Stein–Strömberg theorem
Inequalities in pure mathematics Combinatorics.
- Binomial coefficient bounds
- Factorial bounds
- Fishburn–Shepp inequality
- Fisher's inequality
- Ingleton's inequality
- Lubell–Yamamoto–Meshalkin inequality
- Nesbitt's inequality
- Rearrangement inequality
- Schur's inequality