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Math. Slovaca 61 (2011), No. 4, 1–10
A RELATION OF WEAK MAJORIZATION AND ITS APPLICATIONS
TO CERTAIN INEQUALITIES FOR MEANS
Shan-He Wu, Huan-Nan Shi
ABSTRACT. A relation of weak majorization for n-dimensional real vectors is established, the result is then used to derive some inequalities involving the power mean, the arithmetic mean and the geometric mean in n variables.
2010 Ma thema t i c s Subject Cl a s s i f i c a t ion: Primary 26D15; Secondary 26E60, 52A40.
Ke ywo rds: weak majorization, inequality, Schur-concavity, elementary symmetric function,
power mean, arithmetic mean, geometric mean.
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