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.

55-09_Wu-Shi.pdf